# M.Sc in Statistics with Compulsory Diploma in Actuarial Science

Bharathiar University
In Coimbatore

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MASTER OF PHILOSOPHY IN MATHEMATICS
INTERNATIONAL INSTITUTE OF MANAGEMENT & ENGINEERING

MPhil
Online

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## Important information

Typology | Master |

Start | Coimbatore |

- Master
- Coimbatore

1. To provide a broad based high quality education with combination of the subjects like. Real Analysis, Linear Algebra, Probability, Distributions, Sampling Theory, Object oriented. Programming with C++ and Principles of Insurance to Post-Graduate Degree level for. students who have to demonstrate their ability and potential towards Statistical Theory and. Applications.

Where and when

Starts | Location |
---|---|

On request |
CoimbatoreBharathiar University, Coimbatore, 641046., Tamil Nadu, India See map |

Starts | On request |

Location |
CoimbatoreBharathiar University, Coimbatore, 641046., Tamil Nadu, India See map |

## Course programme

1. To provide a broad based high quality education with combination of the subjects like

Real Analysis, Linear Algebra, Probability, Distributions, Sampling Theory, Object oriented

Programming with C++ and Principles of Insurance to Post-Graduate Degree level for

students who have to demonstrate their ability and potential towards Statistical Theory and

Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector.

3.To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1.An understanding of the Statistical principles, techniques and applications of selected areas

of Statistics and computing.

2.The ability to evaluate, select, write and use of computer software packages for Statistical

theory, which takes into account the needs of the user and constraints towards computing

environment.

3.The ability and confidence to analyze and solve problems both of a routine and of obvious

nature towards applications of Statistical theory.

4.To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation.

08S13A REAL ANALYSIS AND LINEAR ALGEBRA Core - 1

UNIT I

Infinite series: Cauchy's criterion for convergence - alternating series - absolute and

conditional convergence - tests for convergence - comparison test, limit comparison test -

geometric series - integral test - ratio and root test - Dirichelet and Abel's test.

UNIT II

Limit and continuity: limit of a function - algebra of limits - continuity and discontinuity of

function - monotonic function - Bolzano - Weirstrass theorem on continuous functions -

intermediate value theorem - uniform continuity. Derivability of a function - Rolle's theorem

- mean value theorems (Lagrange's, Cauchy's and generalized).

UNIT III

Riemann integral: Riemann integrability of a function. Algebraic properties - integration by

parts - first and second fundamental theorem of integral calculus - first and second mean

value theorems - differentiation under integral sign.

UNIT IV

Finite dimensional vector space - sub-spaces - linear independence - basis and dimension -

inner product space - orthogonality and orthonormal basis - Gram - Schmidt

orthogonalization process. Linear transformations - algebra of matrices, row and column

spaces of a matrix, elementary matrices, determinants, rank and inverse of a matrix, null

space and nullity of a matrix.

UNIT V

Eigen values and eigen vectors of a matrix - characteristic polynomial - Cayley-Hamilton

theorem - minimal polynomial. Quadratic forms - classifications of real quadratic forms -

rank and signature - reduction of a real quadratic form to diagonal form - Sylvester's law of

inertia - some characterizations of positive definite and non-negative definite quadratic forms.

PROBABILITY AND DISTRIBUTIONS

UNIT-I

Probability Spaces and Distribution in Rn, Expectations and Moments, Basic, Markov,

Chebyshev's, Holders, Minkowiski and Jensen's Inequalities. Independence of events and

random Variables, Multiplication Property.

UNIT-II

Convergence of random variables, Convergence in Probability, Almost sure in the rth

mean and in distribution, their relationships, convergence of moments, Helly-Bray

theorem.

Convergence of series of random variables, Kolmogorov's three series theorem, Glivenko-

Cantelli theorem.

UNIT-III

Characteristic functions, its properties, Inversion theorem, Continuity theorem and its

applications.

UNIT-IV

Kinchine's Weak Law of Large Numbers, Strong Law of Large Numbers. Central Limit

Theorem - Statement of CLT, Lindeberg and Levy and Liaponov forms with proof and

Lindeberg-Feller's form without proof and examples.

UNIT-V

Review of Sampling Distributions, Non-central t, F and Chi-Square Distributions and their

properties. Order Statistics, their distributions and properties.

SAMPLING THEORY AND METHODS

UNIT-I

Concept of Sampling Design, Sampling Scheme and Sampling Strategy, Estimator of

Population mean in SRS with replacement. Systematic sampling - Variance of Estimated

mean, Populations in Random order, population with Linear and Period Trend, Auto-

Correlated Populations.

UNIT-II

Des Raj method of Estimation, Murthy's Unordering Principle, Sampling Strategy due to

Rao-Hartley and Cochran, Hartley-Ross Estimator, Midzuno Scheme of Sampling, PPS

Sampling Procedures.

Cluster Sampling-Single Cluster Sampling-Cluster of Equal and Unequal sizes, Two Stage

Cluster Sampling; Mean, Variance, Variance of the Estimated Mean.

UNIT-III

Ratio Estimates-Methods of Estimation, Approximate Variance of Ratio Estimates, Bias of

the Ratio Estimates, Conditions under which the Ratio Estimate is Optimum, Unbiased Ratio-

Type Estimates.

Regression Estimates-Linear Regression Estimates, Regression estimated when computed

from sample, Accuracy of the Variance of Regression Estimates.

UNIT-IV

Double sampling Procedures and repeated surveys, Double Sampling for Stratification

and Optimum Allocation, Regression Estimates-Estimated Variance for Stratification and

Regression Ratio Estimates-Repeated Samplings-Sampling on two occasions, Sampling

on more than two occasions.

UNIT-V

Errors in Surveys-Non Response, types of Non-Response, Call -Backs, a mathematical

model of the effects of Call-Backs adjustment for basis without Call-backs, Mathematical

Model for Errors of Measurement, Interpenetrating sub sample.

OBJECT ORIENTED PROGRAMMING WITH C++ Elective 1

UNIT-I

Principles of Object - Oriented Programming - Software Evolution Procedure and Object

Oriented Paradigm - Basic concepts of Object - Oriented Programming - Benefits of OOP -

Object Oriented Languages - Application of OOP - Beginning with C++ - What is C++?. -

Application of C++ - C++ statements - Structure of C++ Program - Tokens , Expressions

and Control Structures - Tokens - Identifiers - Basic and User - Defined Data Types -

Operators in C++ - Operator Overloading - Operator precedence - Control Structures.

UNIT-II

Functions in C++:- The Main Function - Function Prototyping - Call by Reference - Return

by Reference - Inline functions - Function Overloading - Friend and Virtual Functions -

Classes and Objects - Introduction - Specifying a Class - Defining Member function -

Nesting of Member Function - Private member Functions - Arrays within a Class - Static

Data Members- Static Member Function - Array of Objects - Objects as Function

Arguments, Friendly Functions - Pointers to Members.

UNIT-III

Constructors and Destructors:- Constructors - Copy Constructor Dynamic Constructor-

Constructing Two - Dimensional Arrays - Destructors - Operators Overloading -Type

Conversions.

UNIT-IV

Inheritance, Extending Classes:- Defining Derived classes - Single, Multilevel, Multiple,

Hierarchical and Hybrid inheritance - Virtual Base Classes - Abstract Classes-Pointers,

Virtual Functions and Polymorphism - Pointers to Derived Classes - Virtual Functions.

UNIT-V

Managing Console I/O Operations:-C++ streams - C++ stream Classes - Unformatted I/O

Operations - Formatted Console I/O Operations - Managing output with Manipulators-

Working with Files:- Classes for File Stream Operations- Opening and Closing a File - File Pointers and their manipulators - sequential I/O Operations. Simple Statistical Problems.

PRINCIPLES OF INSURANCE

UNIT-I

Concepts of risk, concept of Insurance, Classification of Insurance, Type of Life Insurance,

pure and terms, Types of general Insurance, Insurance Act, Five, Marine, Motor,

Engineering, Aviation and Agricultural, Alternative Classification, Insurance Property,

Pecuniary interest, liability and person, Distribution between Life and General Insurance.

UNIT-II

History of Insurance in General in India, Economic Principles of Insurance, Legal principles

of Insurance, The Indian contract Act 1872, Insurable interest, Nomination and assignment,

Utmost Good faith, Indemnity, Subrogation, contribution, Proximate cause.

UNIT-III

Representations, Warranties, Conditions

UNIT-IV

Financial Principles, Premium income and outgo investments, Reserves, Surplus, Profit,

Valuation of surplus.

UNIT-V

Theory of rating, Actuarial principles, Mortality tables, Physical and Moral Hazard, Risk

appraisal, Risk selection, Under writing, Reinsurance, concepts and methods.

SEMESTER - II

AIMS:

1. To provide a broad based high quality education with combination of the subjects like

Statistical Inference, Multivariate Analysis, Programming in JAVA, Statistical Practical and Financial Mathematics to Post-Graduate Degree level for students who have to demonstrate

their ability and potential towards Statistical Theory and Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector.

3. To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1. An understanding of the Statistical principles, techniques and applications of selected

areas of Statistics and computing.

2. The ability to evaluate, select, write and use of computer software packages for Statistical

theory which takes into account the needs of the user and constraints towards computing

environment.

3. The ability and confidence to analyze and solve problems both of a routine and of

obvious nature towards applications of Statistical theory.

4. To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation.

08S23A STATISTICAL INFERENCE - I Core 4

UNIT-I

Estimation and point estimation - Sufficiency - Factorization Theorem - minimal

sufficiency, likelihood equivalence - completeness - Uniformly minimum variance unbiased

estimator - Rao-Blackwell and Lehmann-Scheffe's theorems.

UNIT-II

Mean-squared error,Fisher's information measure. Cramer-Rao inequality, Bhattacharya

inequality, Chapman-Robbins inequality - Fisher's information matrix-simultaneous of

parameters in normal(univariate and bivariate) distribution.

UNIT -III

Methods of point estimation-maximum likelihood method(the asymptotic properties of ML

estimators are not included),method of moments, method of minimum chi-square and

modified minimum chi-square.

UNIT-IV

Consistency and CAN estimators. Asymptotic properties of maximum likelihood estimators.

Example of consistent but not asymptotic normal estimators from Pitman family.Information

lower bound for asymptotic variance. Asymptotic relative efficiency. Method of least

squares.

UNIT-V

Interval estimation: Confidence level and confidence coefficient. Duality between acceptance

region of a test and a confidence interval. Pivotal quantity method. Shortest length confidence

intervals.

Construction of confidence intervals for population propotion(small and large samples) and

between two population proportions(large samples)-confidence intervals for mean, variance

of a normal population-difference between mean and ratio of two normal populations.

MULTIVARIATE ANALYSIS

UNIT-I

Reviews of Multivariate Distributions, Multiple and Partial Correlation and Regression,

Multivariate Normal Distribution, Marginal and Conditional Distributions.

UNIT-II

Maximum likelihood Estimators of Parameters, Distribution of Sample Mean Vector, and

Sample Dispersion Matrix, James-Stein Estimator for the Mean Vector, Wishart

Distribution and its Properties (without derivation), Maximum Correlations and their Null

Distributions. Tests based on total, partial and multiple Correlations.

UNIT-III

Tests on Mean Vectors for one and two Multivariate Normal Distributions, Hotelling's T2

and Mahalanobis D2 Distributions, Related Confidence Regions. Testing and Illustration

using likelihood Ratio Criterion.

UNIT-IV

Principal Component Analysis, Factor Analysis Underlying Models and Illustrations,

Identification Problem, Estimation - Maximum likelihood Method, Centroid Method,

Principal Factor Analysis, Estimating Factor/Score, Testing goodness of fit, Rotation of

Factors.

UNIT-V

Classification Analysis using Discriminant Function Hierarchical Clustering: (a)

Agglomerative techniques, Single Linkage Method, Complete Linkage Method,

Incremental Sum of Squares Method, Median Method, Group Average Methods,

Comparison of Methods, Divisive techniques -Monothetic Methods, Polythetic Methods.

PROGRAMMING IN JAVA Elective 2

UNIT I

Java - data types, variables and arrays - Operators - Control statements - Classes - Methods

- Inheritance - Program using these concepts - Package and interfaces.

UNIT - II

Exception handling - Multithreaded programming - Input/Output Basics - Programs using

these concepts.

UNIT - III

String handling - Exploring Java language - utility classes - Exploring Java 1.0

programming using land and 1.0 package.

UNIT - IV

Networks - sockets - reserved sockets - proxy server, internet addressing, Java and Net,

Inetaddress - TCP/IP client sockets, URL, TCP/IP server and client applet basics - class and

architecture - applet skeleton - display methods - handling events - understanding the

HTML - APPLET tag - passing parameters to Applets - AudioClip, Applet stub interface -

Outputting to the console - simple programming examples.

UNIT -V

Introduction to Abstract Window Toolkit (AWT) - working with Windows, Graphics and

Text, AWT controls, Layout managers, menus, images - simple programming examples.

STATISTICAL PRACTICAL - I

The Maximum Mark is 100 with 40 Marks for Internal involving Test and Record

work. 60 Marks for End Examination. The candidate should attend 3 questions out of 4

questions each with 20 Marks with Internal choice. Problem relating to the areas listed below

covered under Semester I and Semester II. The Core Practical-I examination is to be

conducted at the end of the II Semester. The list of topics included for practical are given

below,

1. SAMPLING THEORY AND METHODS:

Simple Random Sampling - Stratified Random Sampling - Systematic Sampling -

Cluster Sampling for Single stage and Two stage - Ratio and Regression estimates - Double

Sampling methods.

2. MULTIVARIATE ANALYSIS:

Test based on Discriminant function - Hotelling T2 Statistic - Mahalanobis D2

Statistic - Principal component analysis -Factor analysis - Single linkage method - complete

linkage method - classification analysis - Divisive techniques.

3. STATISTICAL INFERENCE:

Point Estimation - Maximum Likelihood method - Method of Moments - Minimum

Chi-Square method - Interval estimation

08S2LA Diploma - 2

FINANCIAL MATHEMATICS

UNIT-I

Generalized cash flow model for financial transaction, making allowance for the

probability of payment, Time value of money using the concepts of compound interest and

discounting, Interest rates or discount rates in terms of different time periods.

.

UNIT-II

Calculation of the present value and the accumulated value of a stream of equal or

unequal payments using specified rates of interest and the net present value at a real rate of

interest, assuming a constant rate of inflation.

UNIT-III

Use of compound interest function, Equation of value, Repayment by regular

installments of interest and capital, Discounted cash flow techniques.

UNIT-IV

The investments and risk characteristics of the following types. Simple compound

interest problems, The delivery price and the value of the forward contract using arbitrage

free pricing methods.

UNIT V

Structure of interest rates, Simple Stochastic interest rate models

SEMESTER - III

AIMS:

1. To provide a broad based high quality education with combination of the subjects like

Statistical Inference, Statistical Quality Control, Linear Models, Design of Experiments,

Operations Research, and Practice of Life Assurance to Post-Graduate Degree level for

students who have to demonstrate their ability and potential towards Statistical Theory and

Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector.

3. To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1. An understanding of the Statistical principles, techniques and applications of selected

areas of Statistics and computing.

2. The ability to evaluate, select, write and use of computer software packages for Statistical

theory which takes into account the needs of the user and constraints towards computing

environment.

3. The ability and confidence to analyze and solve problems both of a routine and of

obvious nature towards applications of Statistical theory.

4. To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation.

STATISTICAL INFERENCE-II Core - 7

UNIT-I

Testing of hypotheses: simple and composite hypothese,two types of errors,level of

significance,randomized and non-randomised tests,power and size of a test.Most powerful

test-Neyman-Pearson lemma.Monotone likelihood ratio property-uniformly most powerful

tests.Applicationsto standand statistical distributions.

UNIT-II

Generalization of Nyman-Pearson fundamental lemma(statement only).Unbiased tests-

Construction of uniformly most powerful unbiased tests for one-parameter and multiparameter

exponential families-applications to standard statistical distribution-similar

regions.Locally most powerful(LMP)test-LMP unbiased test.

UNIT-III

Invariance-maximal invariant statistic-invariant test. Likelihood ratio(LR)test-asymptotic

distribution of LR test statistic-consistency of LR test-Construction of LR tests for standard

statistical distributions. Analysis of variance(one-way).Bartlett's test for homogeneity of

variances.

UNIT-IV

U statistic and its property as an estimator of its expected value.Tests for goodness of fit-Chisquare

and Kolmogorov-Smirvon tests. Test for randomness. Wilcoxon's signed-rank test.

Kolmogorov-Smirvon two samplr test. Mann-Whitney U test. Kruskal-Wallis test.

UNIT-V

Introduction to sequential procedures - Stopping times - Wald's equation. SPRT: termination

property, approximation to stopping bounds and applications to standards distributions.

Statement of Wald's fundamental identity. OC and ASN functions and their plotting

STATISTICAL QUALITY CONTROL

UNIT-I

Shewhart Control Charts for X, R, np, p, c etc., and their uses, OC and ARL of Control

Charts, Control Charts based on C.V., Modified Control Charts, CUSUM procedures, use

of V-mask, Derivation of ARL.

UNIT-II

Decision Interval Schemes for CUSUM charts. Economic Designs of Control Charts,

Pre-control, Relative Precision and Process Capability analysis and Gauge capability

analysis, Multivariate Control charts c 2 and Hotelling T2

.

UNIT-III

Basic Concepts of Acceptance Sampling, Single, Double, Multiple and Sequential

Sampling Plans for Attributes, Curtailed and Semi Curtailed Sampling. Dodge-Romig

Tables-LTPD and AOQL protection (Single Sampling Plan only). MIL-STD-105D.

UNIT-IV

Variable Sampling: Assumptions, Single and Double Variable Sampling Plans.

Application of Normal and Non-central t-Distributions in Variable Sampling. Continuous

Sampling Plans:CSP-1, CSP-2 and CSP-3. Special Purpose Plans: Chain Sampling Plans,

Skip-lot Plans.

UNIT-V

Concept : Hazard Function and Reliability Function. Exponential, Gamma and Weibull

Failure Models.Models for wearout failures. System Reliability-Serial, parallel and mixed

systems.

LINEAR MODELS AND DESIGN OF EXPERIMENTS

UNIT-I

Linear Models and Linear Model Assumptions on Error Components-Fixed/Mixed and

Random Component Models-Gauss-Markov set up and its generalization-Linear estimation-

Gauss-Markov theorem-BLUE-Test for Linear Hypothesis- Analysis of Covariance-

Multiple Comparisons - Multiple Range Tests.

UNIT-II

Review of Basic Designs and Principles of Experimentation CRD-RBD-LSD. Construction

of Orthogonal - Analysis of Graeco Latin Squares, Cross Over Designs, Split Plot and Strip

Plot Designs.

UNIT-III

Construction and Analysis of Factorial Experiments Symmetrical and Asymmetrical

Factorial-2n, 3n, Sn and pxp Experiments - Concept and Principle of total, partial and

balanced Confounding in Symmetrical Factorial.

UNIT-IV

Concept of Fractional Replication in Symmetrical Factorial 1/2 and 1/4 in replicate of 2n, 1/s

replicate of Sn Construction and Analysis. Concept of Orthogonal Arrays.

Response Surface experiments - first and second order Rotatable Designs and their

Construction.

UNIT-V

Analysis of Block Designs, C-matrix and its properties, Concept of Connectedness and

Orthogonality Simple and Balanced Lattice Designs-Balanced Incomplete Block Designs-

Youden Square Design, Partially Balanced Incomplete Block Designs and its Classification,

Group Divisible Designs.

OPERATIONS RESEARCH

UNIT-I

Review of LP problems -Methods using Artificial Variables- Two Phase Method -

Principle of Duality-Dual Simplex Method- Transportation and Assignment Problems-

Travelling Salesman Problem- Degeneracy and cycling.

UNIT-II

Games in Normal and Extended Forms, Fundamental Theorem of Matrix Games(without

proof), Solution of 2 x 2, 2 x m and m x n, Zero Sum Games by Dominance Principle, LP

Representation and Graphical Methods. Sequencing and Scheduling Models, 2 Machine njob

problem (no passing), 3 Machine n-job problems.

UNIT-III

Introduction to Networks, Determination of Flows and of Critical Path, PERT, Multistage

Decision Processes and Dynamic Programming, Delman's Principle.

UNIT-IV

Analytic Structure of Inventory Problems, EOQ formula, its Sensitivity Analysis and

Extensions allowing Quantity Discounts and Shortages. Multi-Item Inventory subject to

Constraints, Models with Random Demand, The Static Risk Model P and Q Systems with

constant and Random Lead Times.

UNIT-V

Queueing Models-Specifications and Effectiveness Measures. The M/M/1, M/M/C and

M/C/1 Queues and their steady state Solutions, Machine Interference Problems,

Waiting Time Distributions for M/M/1 and M/M/C Models.

PRACTICE OF LIFE ASSURANCE

UNIT-I

Life insurance organization, The Indian context, The Distribution system, function of

appointment and continuance of agency, remuneration of agents, trends in life insurance

distribution channels.

UNIT-II

Plans of Life insurance, need levels, term life increasing, decreasing term policy, whole life

insurance endowment insurance, money back endowment plan, marriage endowment plan,

education annuity plan, children deferred assurance plans annuities.

UNIT-III

Group insurance, nature of group insurance types of group insurance, gratuity liability, group

superannuating scheme, other group schemes, social security schemes, other special need

plan, industrial life insurance salary saving scheme, disability plans.

UNIT-IV

Application and acceptance, prospectus, proposal forms and other related documents, age

proof, special reports, policy documents, need and format, preamble operative conditions

clauses, proviso, schedule, attestation conditions and privileges, alteration duplicate policy,

premium, premium calculation, days of grace, non-forfeiture options, lapse and revival

schemes.

UNIT-V

Assignment nomination loans, surrenders, foreclosures, Married women's property act

policy, calculations, policy claims, maturity claims, survival benefit payments, death claims,

waiver of evidence of title, early claims, claim concession, presumption of death accident

benefit and disability benefit settlements options valuations and bonus, distribution of

surplus, Types of reinsurance, exchange control regulations payment of premia payment

claims etc., assignment in favor of non-residents deposit export of polices

SEMESTER - IV

AIMS:

1. To provide a broad based high quality education with combination of the subjects like

Time Series, Stochastic Process, Application of Statistical Software Packages, Statistical

Practical, Project-Viva voce and Insurance Business Environment to Post-Graduate Degree

level for students who have to demonstrate their ability and potential towards Statistical

Theory and Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector

3. To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1. An understanding of the Statistical principles, techniques and applications of selected

areas of Statistics and computing.

2. The ability to evaluate, select, write and use of computer software packages for Statistical

theory which takes into account the needs of the user and constraints towards computing

environment.

3. The ability and confidence to analyze and solve problems both of a routine and of

obvious nature towards applications of Statistical theory.

4. To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation

TIME SERIES AND STOCHASTIC PROCESSES

UNIT-I

Introduction to Stochastic Process, Classification of Stochastic Process. Countable

State Markov Chain. Chapman-Kolmogorov's Equations, Calculation of n-step Transition

Probability and its limit. Stationary Distribution, Classification of States, Transient

Markov chain, Random Walk and Gambler's Ruin Problem.

UNIT-II

Continuous Time Markov Process: Kolmogorov Differential Equations, Poisson

Process, Birth and Death Process, Applications to queues and Storage problems.

UNIT-III

Discrete Parameter Stochastic Process/time series. Auto- Covariance and Auto-correlation

and their properties.

UNIT-IV

Detailed study of the stationary process like (a) Moving Average, (b) Autoregressive, (c)

Autoregressive moving average. (d)Autoregressive Integrated Moving Average, Box Jenkins

Models, Brief discussion of Estimation and Related Large Sample theory of the mean.

UNIT-V

Choice of AR and MA terms. Brief discussion of techniques of the ARIMA model

parameters and forecasting. Study of Residuals and Diagnostic Checking.

APPLICATION OF STATISTICAL SOFTWARE PACKAGES

UNIT-I

Introduction to Excel - Various Distributions - Descriptive Statistics - Data analysis tools -

ANOVA - Covariance - Regression - Correlation - Non parametric tests -- Time series

analysis - Using Macros

UNIT-II

Introduction to SPSS 10.0 Icons - Opening files - File extension - Working with Data -

Summarizing Data and Printing - Hypothesis Testing - Descriptive statistics for qualitative

and quantitative data - Graphs and Charts - Regression and Correlation Analysis - Simple

Correlation - scatter diagram, Simple Regression - scatter diagram, Simple Regression -

Estimation and Interpretation of results, Multiple Regression Scatter plot Matrix - Multiple

Regression - Estimation and Testing of Hypothesis - Time Series Analysis and Forecasting -

Linear Trend - Non - Linear Trend - Seasonality -Forecasting with Linear Trend and

regression Models - Index Numbers.

UNIT-III

Introduction to MINITAB 14.2 - Preliminary data analysis - Descriptive statistics -

Probability theory - Inferential Statistics for single through multiple samples.

UNIT-IV

Introduction to STATISTICA 7- Basic Statistical Analysis Methods - ANOVA -

Nonparametric - Distribution Fitting - Multiple Regression - General Linear / Nonlinear

models - General Regression Models - Time Series and Forecasting models - Cluster,

Factor, Principal Component and Discriminant Analysis - Quality Control Charts -

Experimental Design (DOE) - Process Analysis

UNIT-V

Case studies - Problem Solving and Applications of SPSS, Statistical Process Control,

MINITAB, STATISTICA and MS Excel

STATISTICAL PRACTICAL - II

The Maximum Mark is 100 with 40 Marks for Internal involving Test and Record

work. 60 Marks for End Examination. The candidate should attend 3 questions out of 4

questions each with 20 Marks with Internal choice. Problem relating to the areas listed below

covered under Semester III and Semester IV. The Core Practical II examination is to be

conducted at the end of the IV Semester. The list of topics included for practical are given

below,

1. STATISTICAL INFERENCE:

Most powerful test - Uniformly Most Powerful test - Likelihood Ratio test - Chi-Square

goodness of fit test - Non-parametric Tests

2. STATISTICAL QUALITY CONTROL:

Control Charts for X, R, p, np, c and u charts - Single Sampling plan - Double Sampling

Plan - Sequential Sampling Plan - Reliability on type I censoring, type II censoring and

complete censoring.

3. LINEAR MODELS AND DESIGN OF EXPERIMENTS:

Linear Models and Estimation of BLUE - Analysis of Covariance - Greaco Latin Square

Design - Split plot and Strip plot techniques - 2n and 3n factorial experiments with and

without total and partial confounding - BIBD - PBIBD - Youden Square Design - Lattice

Design.

4. OPERATIONS RESEARCH:

Artificial Variable - Dual Simplex methods - Game with and without saddle point -

Dominance principle and job sequencing problems - PERT and CPM techniques - Inventory

problems - Queueing problems.

INSURANCE BUSINESS ENVIRONMENT

UNIT I

Laws to the regulation of Insurance business in India. The Insurance Act 1938, The IRDA ACT

1999, LIC of India ACT 1956 and General Insurance Business ACT 1972. Motor vehicles ACT

1939, Public Liability Insurance ACT 1991, Marine Insurance ACT 1963, Carriage of goods

ACT 1925 etc, including consumer protection ACT 1986.

UNIT II

The economic environment vis-à-vis national Income, Various five year plans, Effect of

inflation, recession, fiscal policy, VAT, Information Technology, Indian Agricultural sector,

Natural resources, Railways

UNIT III

Social and political environment, constitution of India, social Milien, Population education,

Health, industrial environment in the socialistic pattern, economic reforms in India,

globalization, Role of public sector, automobile, aviation, pharma, Biotech, International trade,

WTO.

UNIT IV

The commercial environment & Financial environment, partnership, Cooperative organizations,

companies ACT 1956, Money, Monetary policy, financial institutions, Narasimham committee,

Mutual funds, stock exchanges

UNIT V

Office organization, methods of filing, business correspondence, structure of business letters,

controls, insurance business ABROAD, pensions.

BIO-STATISTICS

UNIT-I

Nature of biological and Clinical experiments and data - Classification of data -Need and

nature of tabulation - Charts and Diagrams for data - Bar diagrams, pie diagrams, pictograms,

histograms-frequency curves and their use.

UNIT-II

Measures of Central tendency - Mean, Median, Mode, Geometric mean, Use of these

averages in biological Studies.

Measures of deviation and Standard deviation - Co-efficient of variation -Measure of

Skewness and Kurtosis.

UNIT-III

Correlation and regression theory - Correlation coefficient - rank correlation -Regression

equations (only problems) - Multiple and Partial correlation and regression.

Basic concepts of sampling - Simple random sample - Stratified sample -Systematic samples.

UNIT-IV

Test of significance based on large sample test: for mean - Variance and proportions-test for

means, Variance and attributes using t, F and Chi-Square distribution. Test for correlation

regression coefficients, Chi-Square test for goodness of fit.

UNIT-V

Analysis of variance: One way and two way Classifications - Completely Randomized blocks

- Randomized Block Design and Latin Square Design (Simple problems based on biological

and biochemical data).

PROBABILITY AND STATISTICS

UNIT-I

Sample spaces - events - Probability axioms - Conditional Probability - Independent events

- Baye's formula- Random Variables - Distribution functions - Marginal distributions,

Conditional distribution - Stochastic Independence. Expectation - Conditional expectation

and Conditional Variance. Moment generating functions - Cumulant generating functions.

UNIT-II

Probabilty distributions - Binomial,Poisson,geometric, Uniform, exponential, normal,

gamma, beta (generating function, Mean, variance & Simple problems).

Correlation - Regression - Multiple & Partial Correlation & regression(Only Problems).

Probability density function & Properties to t,f, Chi-square distributions.

UNIT-III

Test for means, Variances & attributes using the above distributions large sample tests - tests

for means, Variances & Proportions.

Analysis of Variance: One way and two way classifications - Complete Randomized blocks

- Randomized Block Design and Latin Square Design (Only Problems).

UNIT-IV

Estimation: Point estimation - Characteristics of estimation - Interval estimation - Interval

estimates of Mean, Standard deviation, proportion, difference in Means & ratios of Standard

deviations.

Time series analysis: Trend & Seasonal variations - Box - Components of time Series -

Measurement of trend - linear & Second degree Parabola

UNIT-V

Statistical quality control - Statistical basis for control charts - Control limits - Control

Charts for variables - X,R Charts, Charts for defective - P, nP Charts - charts for defects - C

Charts..

STATISTICS FOR MANAGEMENT

UNIT-I

Nature of quantitative analysis in Management, purpose of Statistics, Measurements,

attributes, Units, Variables, discrete and Continuous.

Need and nature of tabulation-Charts and diagrams for data-Bar diagrams, pie diagrams,

pictograms-frequency curves.

UNIT-II

Measure of Central tendency-Mean, Median, Mode-Measure of dispersion - Quartile

deviation, Mean deviation and Standard deviation-Coefficient of variation-Measureof

Skewness and Kurtosis.

UNIT-III

Concepts of events-probability of events-joint, conditional, Marginal probabilities-

Probabaility distribution of a Random variable-Expected value and variance.

UNIT-IV

Theoretical probability distribution-Binomial, Normal and students t distributions.

UNIT-V

Estimation-population and sample-population parameters-Central Limit and theorem-point

estimate and interval estimates of population mean and population proportion.

Concept and Construction of Index numbers. Understanding Index numbers applicable in

the context of economics, business and Management.

OPERATIONS RESEARCH METHODS

UNIT-I

Linear Programming-Graphical Method for two-dimensional problems-General Problem of

Linear programming-Various definitions-Statements of basic theorems & properties. Phase I

and Phase II of the Simplex Method-Sensitivity analysis-transportation Problem and its

Solution. Assignment Problem and its Solution Duality and Shadow Price.

UNIT-II

Queueing theory: Characteristics of queueing Systems-Steady State M/M/1, M/M/C and

M/M/K queueing Models.

Replacement theory: Replacement of items that deteriorate-Replacement of items that fail -

Group replacement.

UNIT-III

Inventory theory: Costs involved in inventory Problems-Single item deterministic Model-

Economic lot size Models without shortages & with shortages having production rate infinite

& finite.

UNIT-IV

Decision Making:Decision under certainty, uncertainty & under risk. Decision trees-expected

value of Project information & imperfect information.

UNIT-V

PERT & CPM: Arrow networks-time estimates-earliest expected time, latest allowable

occurrence- critical path- probability of meeting scheduled time of completeness of projectscalculations

on CPM networks, various floats for structures- external path-updating projectoperation

time cost trade of curve.

ACTUARIAL STATISTICS

UNIT-I

Elements of Compound Interest (nominal and effective rates of interests). Annuities certain,

Present values, accumulated amounts, deferred annuities - Simple problems.

UNIT-II

Redemption of loans, Sinking funds, The Average yield on the life fund of an insurance

office. Simple Problems.

UNIT-III

The mortality table - construction, characteristics and uses of mortality table . The features of

Indian assured lives, Orientals 1925-1935 mortality tables. The LIC (1961-64) table and the

LIC(1970-7 table - Simple Problems

UNIT-IV

Premiums, general principles, natural premiums, level premiums, office premiums, loading

for expenses. With profit and without profit premiums, adequacy of premiums relative

consistency.

UNIT-V

Life office valuation, General principles, Policy values, Retrospective and prospective

methods of valuation of liabilities. (net premium, gross premium and bounds reserve) Sources

of surplus principle method of surplus.

DESCRIPTIVE STATISTICS

UNIT-I

Origin-Scope-Functions, limitations, uses and Misuses of statistics. Classification and

Tabulation of data, Diagrammatic and graphic representation of data.

UNIT-II

Measure of Central tendency-Measures of Dispersion-relative measures of dispersion-

Skewness and Kurtosis-Lorenz's curve.

UNIT-III

Elementary Probability space-Statistical probability Axiomatic approach to probability-

Finitely additive and countable additive probability functions-Addition and multiplication

theorems-Conditional probability-Bayes theorem-Simple problems

UNIT-IV

Random variables-Discrete and continuous random variables-Distribution function and

probability density function of a random variable-Expectation of a random variable-Addition

and product theorems- Evaluation of standard measures of location, dispersion, Skewness and

Kurtosis

UNIT-V

Simple linear correlation and regression-Regression equations-their properties spearman's

Rank correlation Co-efficient.

DATA ANALYSIS

UNIT-I

Sampling procedure - determination of Sample size and selection of sample formation of

questionnaire- Structured and unstructured questionnaire. Field work- Execution of surveydata

collection, Scaling techniques -Guttman scale-Likert 5 points scale.

UNIT-II

Summarizing data- tabulation- averages- Dispersions- measurement of risk- relative measures

of dispersion-efficiency and consistency- comparison of two or more populations-large

samples test, small sample test - ANOVA - Application of Statistical packages.

UNIT-III

Association of attributes: Chisquare test- correlation-rank difference correlation/biserial

correlation, point biserial correlation. Significance of correlation, rank correlation and

biserial correlation coefficient, partial and multiple correlations. Significance of multiple

regression equation-significance of bo, b1.. bn the liner regression coefficient- application of

statistical packages.

UNIT-IV

Non-parametric tests: Tests for randomness, Run test, Sign test, and Mann Whitney U test.

Wilcoxzon signed rank test. Median test- Statistical packages

UNIT-V

Curve fitting - Curves of type

Y=a+bx+cx2 Y= abx

Y =a+bx+cx Y=a.ebx

Time series -estimates of trend and seasonal variation -forecasting -statistical packages.

STATISTICAL METHODS FOR INDUSTRIES

UNIT-I

Historical development of Statistical Quality Control - Meaning of Quality - improvement -

Quality cost - Total Quality Management - causes of variations - X, R, P and C charts.

UNIT-II

Acceptance sampling plans by Attributes - Single Sampling Plan - Double Sampling Plan -

OC curves - AOQ, ATI curves, Dodge Roaming AOQL and LTPD plans, MIL - STD 105D

plans.

UNIT-III

Variable Sampling Plan - One sided and Two sided specifications - Taguchi philosophy and

contributions to Quality Improvement ( Basic concepts only)

UNIT-IV

Test of significance and design of experiments: Tests based on t, F and chi-square

distributions - Analysis of variance - One way and Two way classification Complete

Randomized Design(CRD), Randomized Block Design(RBD) , Latin Square Design(LSD).

UNIT-V

Basic of reliability theory - Life time distribution - Hazard rate- Survival function-

Exponential, Weibull, Gamma and life time distributions

STATISTICAL METHODS FOR RESEARCHERS

UNIT-I

Definition of Statistics and its applications in various disciplines - Collection of Data -

Classification, Tabulation and graphical representation of data- Construction of univariate

and Bivariate frequency distribution-measures of central tendency-measures of dispersion -

coefficient of variation.

UNIT-II

Random experiment-sample space-events-mathematical and statistical definition of

probability-conditional probability-Baye's theorem-random variable-distribution functionmoments-

Binomial distribution-Poisson distribution-normal distribution and their properties

UNIT-III

Scatter diagram-Karl Pearson's coefficient of correlation - concurrent deviation methodcoefficient

of determination-Spearman's Rank correlation-Linear regression-regression lines.

UNIT-IV

Tests of significance-types of hypotheses-two types of errors-critical region-level of

significance, small sample tests based on t, F distribution, Chi-square test of goodness of fit,

contingency table-test of independence of factors-Large sample tests.

UNIT-V

Test of equality of several populations means, one way and two way analysis of variance.

Non-parametric tests-sign, Run and Median tests-two sample rank test-sampling and its uses,

sampling methods- unrestricted Random sampling (SRS)- Restricted Sampling (Stratified and

Systematic).

STATISTICAL METHODS FOR BIOLOGISTS

UNIT-I

Nature of Biological and Clinical experiments of data-Classification and tabulation of data-

Diagrammatic representation of data- Histogram and frequency curves

UNIT-II

Measures of Central tendency-Mean, Median, Mode, Geometric mean, Harmonic Mean-

Measures of deviation - Range, Mean deviation, Quartile and standard deviation - Measures

of Skewness and Kurtosis.

UNIT-III

Correlation : Rank Correlation - Multiple and Partial Correlation - Regression - Regression

equations for biological problems.

UNIT-IV

Basic concepts of sampling - Simple random sample - Stratified sample - systematic sample

- cluster sample. Test of significance based on large sample - Mean, Variance and

Proportions.

UNIT-V

Analysis of variance -One way and Two way classifications - Completely Randomized

blocks - Randomized Block design and Latin Square Design (Simple problems based on

biological data)

ELEMENTS OF OPERATIONS RESEARCH

UNIT-I

Linear Programming Problem - Graphical Method - General Problem of Linear

Programming - Simplex Method - Phase I and Phase II Problems - Transportation and

Assignment Problems.

UNIT-II

Replacement theory : Replacement of Items that deteriorate - Replacement of items that fail

completely - Individual and group replacement policy.

UNIT-III

Sequencing Theory - Processing 'n' jobs through 2 machines - Processing 'n' jobs through 3

machines - Processing 'n' jobs through 'm' machines.

UNIT-IV

Network Theory - Introduction to Network - Determination and flow for Critical Path

Method - Project Evaluation Review Techniques and its differences.

UNIT-V

Inventory Theory - Meaning of Inventory - Factors involved in Inventory - Economic

Models with and without shortages

Real Analysis, Linear Algebra, Probability, Distributions, Sampling Theory, Object oriented

Programming with C++ and Principles of Insurance to Post-Graduate Degree level for

students who have to demonstrate their ability and potential towards Statistical Theory and

Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector.

3.To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1.An understanding of the Statistical principles, techniques and applications of selected areas

of Statistics and computing.

2.The ability to evaluate, select, write and use of computer software packages for Statistical

theory, which takes into account the needs of the user and constraints towards computing

environment.

3.The ability and confidence to analyze and solve problems both of a routine and of obvious

nature towards applications of Statistical theory.

4.To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation.

08S13A REAL ANALYSIS AND LINEAR ALGEBRA Core - 1

UNIT I

Infinite series: Cauchy's criterion for convergence - alternating series - absolute and

conditional convergence - tests for convergence - comparison test, limit comparison test -

geometric series - integral test - ratio and root test - Dirichelet and Abel's test.

UNIT II

Limit and continuity: limit of a function - algebra of limits - continuity and discontinuity of

function - monotonic function - Bolzano - Weirstrass theorem on continuous functions -

intermediate value theorem - uniform continuity. Derivability of a function - Rolle's theorem

- mean value theorems (Lagrange's, Cauchy's and generalized).

UNIT III

Riemann integral: Riemann integrability of a function. Algebraic properties - integration by

parts - first and second fundamental theorem of integral calculus - first and second mean

value theorems - differentiation under integral sign.

UNIT IV

Finite dimensional vector space - sub-spaces - linear independence - basis and dimension -

inner product space - orthogonality and orthonormal basis - Gram - Schmidt

orthogonalization process. Linear transformations - algebra of matrices, row and column

spaces of a matrix, elementary matrices, determinants, rank and inverse of a matrix, null

space and nullity of a matrix.

UNIT V

Eigen values and eigen vectors of a matrix - characteristic polynomial - Cayley-Hamilton

theorem - minimal polynomial. Quadratic forms - classifications of real quadratic forms -

rank and signature - reduction of a real quadratic form to diagonal form - Sylvester's law of

inertia - some characterizations of positive definite and non-negative definite quadratic forms.

PROBABILITY AND DISTRIBUTIONS

UNIT-I

Probability Spaces and Distribution in Rn, Expectations and Moments, Basic, Markov,

Chebyshev's, Holders, Minkowiski and Jensen's Inequalities. Independence of events and

random Variables, Multiplication Property.

UNIT-II

Convergence of random variables, Convergence in Probability, Almost sure in the rth

mean and in distribution, their relationships, convergence of moments, Helly-Bray

theorem.

Convergence of series of random variables, Kolmogorov's three series theorem, Glivenko-

Cantelli theorem.

UNIT-III

Characteristic functions, its properties, Inversion theorem, Continuity theorem and its

applications.

UNIT-IV

Kinchine's Weak Law of Large Numbers, Strong Law of Large Numbers. Central Limit

Theorem - Statement of CLT, Lindeberg and Levy and Liaponov forms with proof and

Lindeberg-Feller's form without proof and examples.

UNIT-V

Review of Sampling Distributions, Non-central t, F and Chi-Square Distributions and their

properties. Order Statistics, their distributions and properties.

SAMPLING THEORY AND METHODS

UNIT-I

Concept of Sampling Design, Sampling Scheme and Sampling Strategy, Estimator of

Population mean in SRS with replacement. Systematic sampling - Variance of Estimated

mean, Populations in Random order, population with Linear and Period Trend, Auto-

Correlated Populations.

UNIT-II

Des Raj method of Estimation, Murthy's Unordering Principle, Sampling Strategy due to

Rao-Hartley and Cochran, Hartley-Ross Estimator, Midzuno Scheme of Sampling, PPS

Sampling Procedures.

Cluster Sampling-Single Cluster Sampling-Cluster of Equal and Unequal sizes, Two Stage

Cluster Sampling; Mean, Variance, Variance of the Estimated Mean.

UNIT-III

Ratio Estimates-Methods of Estimation, Approximate Variance of Ratio Estimates, Bias of

the Ratio Estimates, Conditions under which the Ratio Estimate is Optimum, Unbiased Ratio-

Type Estimates.

Regression Estimates-Linear Regression Estimates, Regression estimated when computed

from sample, Accuracy of the Variance of Regression Estimates.

UNIT-IV

Double sampling Procedures and repeated surveys, Double Sampling for Stratification

and Optimum Allocation, Regression Estimates-Estimated Variance for Stratification and

Regression Ratio Estimates-Repeated Samplings-Sampling on two occasions, Sampling

on more than two occasions.

UNIT-V

Errors in Surveys-Non Response, types of Non-Response, Call -Backs, a mathematical

model of the effects of Call-Backs adjustment for basis without Call-backs, Mathematical

Model for Errors of Measurement, Interpenetrating sub sample.

OBJECT ORIENTED PROGRAMMING WITH C++ Elective 1

UNIT-I

Principles of Object - Oriented Programming - Software Evolution Procedure and Object

Oriented Paradigm - Basic concepts of Object - Oriented Programming - Benefits of OOP -

Object Oriented Languages - Application of OOP - Beginning with C++ - What is C++?. -

Application of C++ - C++ statements - Structure of C++ Program - Tokens , Expressions

and Control Structures - Tokens - Identifiers - Basic and User - Defined Data Types -

Operators in C++ - Operator Overloading - Operator precedence - Control Structures.

UNIT-II

Functions in C++:- The Main Function - Function Prototyping - Call by Reference - Return

by Reference - Inline functions - Function Overloading - Friend and Virtual Functions -

Classes and Objects - Introduction - Specifying a Class - Defining Member function -

Nesting of Member Function - Private member Functions - Arrays within a Class - Static

Data Members- Static Member Function - Array of Objects - Objects as Function

Arguments, Friendly Functions - Pointers to Members.

UNIT-III

Constructors and Destructors:- Constructors - Copy Constructor Dynamic Constructor-

Constructing Two - Dimensional Arrays - Destructors - Operators Overloading -Type

Conversions.

UNIT-IV

Inheritance, Extending Classes:- Defining Derived classes - Single, Multilevel, Multiple,

Hierarchical and Hybrid inheritance - Virtual Base Classes - Abstract Classes-Pointers,

Virtual Functions and Polymorphism - Pointers to Derived Classes - Virtual Functions.

UNIT-V

Managing Console I/O Operations:-C++ streams - C++ stream Classes - Unformatted I/O

Operations - Formatted Console I/O Operations - Managing output with Manipulators-

Working with Files:- Classes for File Stream Operations- Opening and Closing a File - File Pointers and their manipulators - sequential I/O Operations. Simple Statistical Problems.

PRINCIPLES OF INSURANCE

UNIT-I

Concepts of risk, concept of Insurance, Classification of Insurance, Type of Life Insurance,

pure and terms, Types of general Insurance, Insurance Act, Five, Marine, Motor,

Engineering, Aviation and Agricultural, Alternative Classification, Insurance Property,

Pecuniary interest, liability and person, Distribution between Life and General Insurance.

UNIT-II

History of Insurance in General in India, Economic Principles of Insurance, Legal principles

of Insurance, The Indian contract Act 1872, Insurable interest, Nomination and assignment,

Utmost Good faith, Indemnity, Subrogation, contribution, Proximate cause.

UNIT-III

Representations, Warranties, Conditions

UNIT-IV

Financial Principles, Premium income and outgo investments, Reserves, Surplus, Profit,

Valuation of surplus.

UNIT-V

Theory of rating, Actuarial principles, Mortality tables, Physical and Moral Hazard, Risk

appraisal, Risk selection, Under writing, Reinsurance, concepts and methods.

SEMESTER - II

AIMS:

1. To provide a broad based high quality education with combination of the subjects like

Statistical Inference, Multivariate Analysis, Programming in JAVA, Statistical Practical and Financial Mathematics to Post-Graduate Degree level for students who have to demonstrate

their ability and potential towards Statistical Theory and Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector.

3. To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1. An understanding of the Statistical principles, techniques and applications of selected

areas of Statistics and computing.

2. The ability to evaluate, select, write and use of computer software packages for Statistical

theory which takes into account the needs of the user and constraints towards computing

environment.

3. The ability and confidence to analyze and solve problems both of a routine and of

obvious nature towards applications of Statistical theory.

4. To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation.

08S23A STATISTICAL INFERENCE - I Core 4

UNIT-I

Estimation and point estimation - Sufficiency - Factorization Theorem - minimal

sufficiency, likelihood equivalence - completeness - Uniformly minimum variance unbiased

estimator - Rao-Blackwell and Lehmann-Scheffe's theorems.

UNIT-II

Mean-squared error,Fisher's information measure. Cramer-Rao inequality, Bhattacharya

inequality, Chapman-Robbins inequality - Fisher's information matrix-simultaneous of

parameters in normal(univariate and bivariate) distribution.

UNIT -III

Methods of point estimation-maximum likelihood method(the asymptotic properties of ML

estimators are not included),method of moments, method of minimum chi-square and

modified minimum chi-square.

UNIT-IV

Consistency and CAN estimators. Asymptotic properties of maximum likelihood estimators.

Example of consistent but not asymptotic normal estimators from Pitman family.Information

lower bound for asymptotic variance. Asymptotic relative efficiency. Method of least

squares.

UNIT-V

Interval estimation: Confidence level and confidence coefficient. Duality between acceptance

region of a test and a confidence interval. Pivotal quantity method. Shortest length confidence

intervals.

Construction of confidence intervals for population propotion(small and large samples) and

between two population proportions(large samples)-confidence intervals for mean, variance

of a normal population-difference between mean and ratio of two normal populations.

MULTIVARIATE ANALYSIS

UNIT-I

Reviews of Multivariate Distributions, Multiple and Partial Correlation and Regression,

Multivariate Normal Distribution, Marginal and Conditional Distributions.

UNIT-II

Maximum likelihood Estimators of Parameters, Distribution of Sample Mean Vector, and

Sample Dispersion Matrix, James-Stein Estimator for the Mean Vector, Wishart

Distribution and its Properties (without derivation), Maximum Correlations and their Null

Distributions. Tests based on total, partial and multiple Correlations.

UNIT-III

Tests on Mean Vectors for one and two Multivariate Normal Distributions, Hotelling's T2

and Mahalanobis D2 Distributions, Related Confidence Regions. Testing and Illustration

using likelihood Ratio Criterion.

UNIT-IV

Principal Component Analysis, Factor Analysis Underlying Models and Illustrations,

Identification Problem, Estimation - Maximum likelihood Method, Centroid Method,

Principal Factor Analysis, Estimating Factor/Score, Testing goodness of fit, Rotation of

Factors.

UNIT-V

Classification Analysis using Discriminant Function Hierarchical Clustering: (a)

Agglomerative techniques, Single Linkage Method, Complete Linkage Method,

Incremental Sum of Squares Method, Median Method, Group Average Methods,

Comparison of Methods, Divisive techniques -Monothetic Methods, Polythetic Methods.

PROGRAMMING IN JAVA Elective 2

UNIT I

Java - data types, variables and arrays - Operators - Control statements - Classes - Methods

- Inheritance - Program using these concepts - Package and interfaces.

UNIT - II

Exception handling - Multithreaded programming - Input/Output Basics - Programs using

these concepts.

UNIT - III

String handling - Exploring Java language - utility classes - Exploring Java 1.0

programming using land and 1.0 package.

UNIT - IV

Networks - sockets - reserved sockets - proxy server, internet addressing, Java and Net,

Inetaddress - TCP/IP client sockets, URL, TCP/IP server and client applet basics - class and

architecture - applet skeleton - display methods - handling events - understanding the

HTML - APPLET tag - passing parameters to Applets - AudioClip, Applet stub interface -

Outputting to the console - simple programming examples.

UNIT -V

Introduction to Abstract Window Toolkit (AWT) - working with Windows, Graphics and

Text, AWT controls, Layout managers, menus, images - simple programming examples.

STATISTICAL PRACTICAL - I

The Maximum Mark is 100 with 40 Marks for Internal involving Test and Record

work. 60 Marks for End Examination. The candidate should attend 3 questions out of 4

questions each with 20 Marks with Internal choice. Problem relating to the areas listed below

covered under Semester I and Semester II. The Core Practical-I examination is to be

conducted at the end of the II Semester. The list of topics included for practical are given

below,

1. SAMPLING THEORY AND METHODS:

Simple Random Sampling - Stratified Random Sampling - Systematic Sampling -

Cluster Sampling for Single stage and Two stage - Ratio and Regression estimates - Double

Sampling methods.

2. MULTIVARIATE ANALYSIS:

Test based on Discriminant function - Hotelling T2 Statistic - Mahalanobis D2

Statistic - Principal component analysis -Factor analysis - Single linkage method - complete

linkage method - classification analysis - Divisive techniques.

3. STATISTICAL INFERENCE:

Point Estimation - Maximum Likelihood method - Method of Moments - Minimum

Chi-Square method - Interval estimation

08S2LA Diploma - 2

FINANCIAL MATHEMATICS

UNIT-I

Generalized cash flow model for financial transaction, making allowance for the

probability of payment, Time value of money using the concepts of compound interest and

discounting, Interest rates or discount rates in terms of different time periods.

.

UNIT-II

Calculation of the present value and the accumulated value of a stream of equal or

unequal payments using specified rates of interest and the net present value at a real rate of

interest, assuming a constant rate of inflation.

UNIT-III

Use of compound interest function, Equation of value, Repayment by regular

installments of interest and capital, Discounted cash flow techniques.

UNIT-IV

The investments and risk characteristics of the following types. Simple compound

interest problems, The delivery price and the value of the forward contract using arbitrage

free pricing methods.

UNIT V

Structure of interest rates, Simple Stochastic interest rate models

SEMESTER - III

AIMS:

1. To provide a broad based high quality education with combination of the subjects like

Statistical Inference, Statistical Quality Control, Linear Models, Design of Experiments,

Operations Research, and Practice of Life Assurance to Post-Graduate Degree level for

students who have to demonstrate their ability and potential towards Statistical Theory and

Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector.

3. To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1. An understanding of the Statistical principles, techniques and applications of selected

areas of Statistics and computing.

2. The ability to evaluate, select, write and use of computer software packages for Statistical

theory which takes into account the needs of the user and constraints towards computing

environment.

3. The ability and confidence to analyze and solve problems both of a routine and of

obvious nature towards applications of Statistical theory.

4. To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation.

STATISTICAL INFERENCE-II Core - 7

UNIT-I

Testing of hypotheses: simple and composite hypothese,two types of errors,level of

significance,randomized and non-randomised tests,power and size of a test.Most powerful

test-Neyman-Pearson lemma.Monotone likelihood ratio property-uniformly most powerful

tests.Applicationsto standand statistical distributions.

UNIT-II

Generalization of Nyman-Pearson fundamental lemma(statement only).Unbiased tests-

Construction of uniformly most powerful unbiased tests for one-parameter and multiparameter

exponential families-applications to standard statistical distribution-similar

regions.Locally most powerful(LMP)test-LMP unbiased test.

UNIT-III

Invariance-maximal invariant statistic-invariant test. Likelihood ratio(LR)test-asymptotic

distribution of LR test statistic-consistency of LR test-Construction of LR tests for standard

statistical distributions. Analysis of variance(one-way).Bartlett's test for homogeneity of

variances.

UNIT-IV

U statistic and its property as an estimator of its expected value.Tests for goodness of fit-Chisquare

and Kolmogorov-Smirvon tests. Test for randomness. Wilcoxon's signed-rank test.

Kolmogorov-Smirvon two samplr test. Mann-Whitney U test. Kruskal-Wallis test.

UNIT-V

Introduction to sequential procedures - Stopping times - Wald's equation. SPRT: termination

property, approximation to stopping bounds and applications to standards distributions.

Statement of Wald's fundamental identity. OC and ASN functions and their plotting

STATISTICAL QUALITY CONTROL

UNIT-I

Shewhart Control Charts for X, R, np, p, c etc., and their uses, OC and ARL of Control

Charts, Control Charts based on C.V., Modified Control Charts, CUSUM procedures, use

of V-mask, Derivation of ARL.

UNIT-II

Decision Interval Schemes for CUSUM charts. Economic Designs of Control Charts,

Pre-control, Relative Precision and Process Capability analysis and Gauge capability

analysis, Multivariate Control charts c 2 and Hotelling T2

.

UNIT-III

Basic Concepts of Acceptance Sampling, Single, Double, Multiple and Sequential

Sampling Plans for Attributes, Curtailed and Semi Curtailed Sampling. Dodge-Romig

Tables-LTPD and AOQL protection (Single Sampling Plan only). MIL-STD-105D.

UNIT-IV

Variable Sampling: Assumptions, Single and Double Variable Sampling Plans.

Application of Normal and Non-central t-Distributions in Variable Sampling. Continuous

Sampling Plans:CSP-1, CSP-2 and CSP-3. Special Purpose Plans: Chain Sampling Plans,

Skip-lot Plans.

UNIT-V

Concept : Hazard Function and Reliability Function. Exponential, Gamma and Weibull

Failure Models.Models for wearout failures. System Reliability-Serial, parallel and mixed

systems.

LINEAR MODELS AND DESIGN OF EXPERIMENTS

UNIT-I

Linear Models and Linear Model Assumptions on Error Components-Fixed/Mixed and

Random Component Models-Gauss-Markov set up and its generalization-Linear estimation-

Gauss-Markov theorem-BLUE-Test for Linear Hypothesis- Analysis of Covariance-

Multiple Comparisons - Multiple Range Tests.

UNIT-II

Review of Basic Designs and Principles of Experimentation CRD-RBD-LSD. Construction

of Orthogonal - Analysis of Graeco Latin Squares, Cross Over Designs, Split Plot and Strip

Plot Designs.

UNIT-III

Construction and Analysis of Factorial Experiments Symmetrical and Asymmetrical

Factorial-2n, 3n, Sn and pxp Experiments - Concept and Principle of total, partial and

balanced Confounding in Symmetrical Factorial.

UNIT-IV

Concept of Fractional Replication in Symmetrical Factorial 1/2 and 1/4 in replicate of 2n, 1/s

replicate of Sn Construction and Analysis. Concept of Orthogonal Arrays.

Response Surface experiments - first and second order Rotatable Designs and their

Construction.

UNIT-V

Analysis of Block Designs, C-matrix and its properties, Concept of Connectedness and

Orthogonality Simple and Balanced Lattice Designs-Balanced Incomplete Block Designs-

Youden Square Design, Partially Balanced Incomplete Block Designs and its Classification,

Group Divisible Designs.

OPERATIONS RESEARCH

UNIT-I

Review of LP problems -Methods using Artificial Variables- Two Phase Method -

Principle of Duality-Dual Simplex Method- Transportation and Assignment Problems-

Travelling Salesman Problem- Degeneracy and cycling.

UNIT-II

Games in Normal and Extended Forms, Fundamental Theorem of Matrix Games(without

proof), Solution of 2 x 2, 2 x m and m x n, Zero Sum Games by Dominance Principle, LP

Representation and Graphical Methods. Sequencing and Scheduling Models, 2 Machine njob

problem (no passing), 3 Machine n-job problems.

UNIT-III

Introduction to Networks, Determination of Flows and of Critical Path, PERT, Multistage

Decision Processes and Dynamic Programming, Delman's Principle.

UNIT-IV

Analytic Structure of Inventory Problems, EOQ formula, its Sensitivity Analysis and

Extensions allowing Quantity Discounts and Shortages. Multi-Item Inventory subject to

Constraints, Models with Random Demand, The Static Risk Model P and Q Systems with

constant and Random Lead Times.

UNIT-V

Queueing Models-Specifications and Effectiveness Measures. The M/M/1, M/M/C and

M/C/1 Queues and their steady state Solutions, Machine Interference Problems,

Waiting Time Distributions for M/M/1 and M/M/C Models.

PRACTICE OF LIFE ASSURANCE

UNIT-I

Life insurance organization, The Indian context, The Distribution system, function of

appointment and continuance of agency, remuneration of agents, trends in life insurance

distribution channels.

UNIT-II

Plans of Life insurance, need levels, term life increasing, decreasing term policy, whole life

insurance endowment insurance, money back endowment plan, marriage endowment plan,

education annuity plan, children deferred assurance plans annuities.

UNIT-III

Group insurance, nature of group insurance types of group insurance, gratuity liability, group

superannuating scheme, other group schemes, social security schemes, other special need

plan, industrial life insurance salary saving scheme, disability plans.

UNIT-IV

Application and acceptance, prospectus, proposal forms and other related documents, age

proof, special reports, policy documents, need and format, preamble operative conditions

clauses, proviso, schedule, attestation conditions and privileges, alteration duplicate policy,

premium, premium calculation, days of grace, non-forfeiture options, lapse and revival

schemes.

UNIT-V

Assignment nomination loans, surrenders, foreclosures, Married women's property act

policy, calculations, policy claims, maturity claims, survival benefit payments, death claims,

waiver of evidence of title, early claims, claim concession, presumption of death accident

benefit and disability benefit settlements options valuations and bonus, distribution of

surplus, Types of reinsurance, exchange control regulations payment of premia payment

claims etc., assignment in favor of non-residents deposit export of polices

SEMESTER - IV

AIMS:

1. To provide a broad based high quality education with combination of the subjects like

Time Series, Stochastic Process, Application of Statistical Software Packages, Statistical

Practical, Project-Viva voce and Insurance Business Environment to Post-Graduate Degree

level for students who have to demonstrate their ability and potential towards Statistical

Theory and Applications.

2. To develop knowledge, understanding and experience of the theory, practice and

application of selected areas of statistical computing and to produce graduates needed by

public and private sector to help and solve practical problems using the skills and techniques

of these areas and to develop analytical skills for Insurance Sector

3. To develop enterprise competences emphasizing the key skills of learning and

communication for Statistical theory.

OBJECTIVES:

1. An understanding of the Statistical principles, techniques and applications of selected

areas of Statistics and computing.

2. The ability to evaluate, select, write and use of computer software packages for Statistical

theory which takes into account the needs of the user and constraints towards computing

environment.

3. The ability and confidence to analyze and solve problems both of a routine and of

obvious nature towards applications of Statistical theory.

4. To gain deeper understanding, problem solving skills and greater knowledge of selected

topics in statistical computation

TIME SERIES AND STOCHASTIC PROCESSES

UNIT-I

Introduction to Stochastic Process, Classification of Stochastic Process. Countable

State Markov Chain. Chapman-Kolmogorov's Equations, Calculation of n-step Transition

Probability and its limit. Stationary Distribution, Classification of States, Transient

Markov chain, Random Walk and Gambler's Ruin Problem.

UNIT-II

Continuous Time Markov Process: Kolmogorov Differential Equations, Poisson

Process, Birth and Death Process, Applications to queues and Storage problems.

UNIT-III

Discrete Parameter Stochastic Process/time series. Auto- Covariance and Auto-correlation

and their properties.

UNIT-IV

Detailed study of the stationary process like (a) Moving Average, (b) Autoregressive, (c)

Autoregressive moving average. (d)Autoregressive Integrated Moving Average, Box Jenkins

Models, Brief discussion of Estimation and Related Large Sample theory of the mean.

UNIT-V

Choice of AR and MA terms. Brief discussion of techniques of the ARIMA model

parameters and forecasting. Study of Residuals and Diagnostic Checking.

APPLICATION OF STATISTICAL SOFTWARE PACKAGES

UNIT-I

Introduction to Excel - Various Distributions - Descriptive Statistics - Data analysis tools -

ANOVA - Covariance - Regression - Correlation - Non parametric tests -- Time series

analysis - Using Macros

UNIT-II

Introduction to SPSS 10.0 Icons - Opening files - File extension - Working with Data -

Summarizing Data and Printing - Hypothesis Testing - Descriptive statistics for qualitative

and quantitative data - Graphs and Charts - Regression and Correlation Analysis - Simple

Correlation - scatter diagram, Simple Regression - scatter diagram, Simple Regression -

Estimation and Interpretation of results, Multiple Regression Scatter plot Matrix - Multiple

Regression - Estimation and Testing of Hypothesis - Time Series Analysis and Forecasting -

Linear Trend - Non - Linear Trend - Seasonality -Forecasting with Linear Trend and

regression Models - Index Numbers.

UNIT-III

Introduction to MINITAB 14.2 - Preliminary data analysis - Descriptive statistics -

Probability theory - Inferential Statistics for single through multiple samples.

UNIT-IV

Introduction to STATISTICA 7- Basic Statistical Analysis Methods - ANOVA -

Nonparametric - Distribution Fitting - Multiple Regression - General Linear / Nonlinear

models - General Regression Models - Time Series and Forecasting models - Cluster,

Factor, Principal Component and Discriminant Analysis - Quality Control Charts -

Experimental Design (DOE) - Process Analysis

UNIT-V

Case studies - Problem Solving and Applications of SPSS, Statistical Process Control,

MINITAB, STATISTICA and MS Excel

STATISTICAL PRACTICAL - II

The Maximum Mark is 100 with 40 Marks for Internal involving Test and Record

work. 60 Marks for End Examination. The candidate should attend 3 questions out of 4

questions each with 20 Marks with Internal choice. Problem relating to the areas listed below

covered under Semester III and Semester IV. The Core Practical II examination is to be

conducted at the end of the IV Semester. The list of topics included for practical are given

below,

1. STATISTICAL INFERENCE:

Most powerful test - Uniformly Most Powerful test - Likelihood Ratio test - Chi-Square

goodness of fit test - Non-parametric Tests

2. STATISTICAL QUALITY CONTROL:

Control Charts for X, R, p, np, c and u charts - Single Sampling plan - Double Sampling

Plan - Sequential Sampling Plan - Reliability on type I censoring, type II censoring and

complete censoring.

3. LINEAR MODELS AND DESIGN OF EXPERIMENTS:

Linear Models and Estimation of BLUE - Analysis of Covariance - Greaco Latin Square

Design - Split plot and Strip plot techniques - 2n and 3n factorial experiments with and

without total and partial confounding - BIBD - PBIBD - Youden Square Design - Lattice

Design.

4. OPERATIONS RESEARCH:

Artificial Variable - Dual Simplex methods - Game with and without saddle point -

Dominance principle and job sequencing problems - PERT and CPM techniques - Inventory

problems - Queueing problems.

INSURANCE BUSINESS ENVIRONMENT

UNIT I

Laws to the regulation of Insurance business in India. The Insurance Act 1938, The IRDA ACT

1999, LIC of India ACT 1956 and General Insurance Business ACT 1972. Motor vehicles ACT

1939, Public Liability Insurance ACT 1991, Marine Insurance ACT 1963, Carriage of goods

ACT 1925 etc, including consumer protection ACT 1986.

UNIT II

The economic environment vis-à-vis national Income, Various five year plans, Effect of

inflation, recession, fiscal policy, VAT, Information Technology, Indian Agricultural sector,

Natural resources, Railways

UNIT III

Social and political environment, constitution of India, social Milien, Population education,

Health, industrial environment in the socialistic pattern, economic reforms in India,

globalization, Role of public sector, automobile, aviation, pharma, Biotech, International trade,

WTO.

UNIT IV

The commercial environment & Financial environment, partnership, Cooperative organizations,

companies ACT 1956, Money, Monetary policy, financial institutions, Narasimham committee,

Mutual funds, stock exchanges

UNIT V

Office organization, methods of filing, business correspondence, structure of business letters,

controls, insurance business ABROAD, pensions.

BIO-STATISTICS

UNIT-I

Nature of biological and Clinical experiments and data - Classification of data -Need and

nature of tabulation - Charts and Diagrams for data - Bar diagrams, pie diagrams, pictograms,

histograms-frequency curves and their use.

UNIT-II

Measures of Central tendency - Mean, Median, Mode, Geometric mean, Use of these

averages in biological Studies.

Measures of deviation and Standard deviation - Co-efficient of variation -Measure of

Skewness and Kurtosis.

UNIT-III

Correlation and regression theory - Correlation coefficient - rank correlation -Regression

equations (only problems) - Multiple and Partial correlation and regression.

Basic concepts of sampling - Simple random sample - Stratified sample -Systematic samples.

UNIT-IV

Test of significance based on large sample test: for mean - Variance and proportions-test for

means, Variance and attributes using t, F and Chi-Square distribution. Test for correlation

regression coefficients, Chi-Square test for goodness of fit.

UNIT-V

Analysis of variance: One way and two way Classifications - Completely Randomized blocks

- Randomized Block Design and Latin Square Design (Simple problems based on biological

and biochemical data).

PROBABILITY AND STATISTICS

UNIT-I

Sample spaces - events - Probability axioms - Conditional Probability - Independent events

- Baye's formula- Random Variables - Distribution functions - Marginal distributions,

Conditional distribution - Stochastic Independence. Expectation - Conditional expectation

and Conditional Variance. Moment generating functions - Cumulant generating functions.

UNIT-II

Probabilty distributions - Binomial,Poisson,geometric, Uniform, exponential, normal,

gamma, beta (generating function, Mean, variance & Simple problems).

Correlation - Regression - Multiple & Partial Correlation & regression(Only Problems).

Probability density function & Properties to t,f, Chi-square distributions.

UNIT-III

Test for means, Variances & attributes using the above distributions large sample tests - tests

for means, Variances & Proportions.

Analysis of Variance: One way and two way classifications - Complete Randomized blocks

- Randomized Block Design and Latin Square Design (Only Problems).

UNIT-IV

Estimation: Point estimation - Characteristics of estimation - Interval estimation - Interval

estimates of Mean, Standard deviation, proportion, difference in Means & ratios of Standard

deviations.

Time series analysis: Trend & Seasonal variations - Box - Components of time Series -

Measurement of trend - linear & Second degree Parabola

UNIT-V

Statistical quality control - Statistical basis for control charts - Control limits - Control

Charts for variables - X,R Charts, Charts for defective - P, nP Charts - charts for defects - C

Charts..

STATISTICS FOR MANAGEMENT

UNIT-I

Nature of quantitative analysis in Management, purpose of Statistics, Measurements,

attributes, Units, Variables, discrete and Continuous.

Need and nature of tabulation-Charts and diagrams for data-Bar diagrams, pie diagrams,

pictograms-frequency curves.

UNIT-II

Measure of Central tendency-Mean, Median, Mode-Measure of dispersion - Quartile

deviation, Mean deviation and Standard deviation-Coefficient of variation-Measureof

Skewness and Kurtosis.

UNIT-III

Concepts of events-probability of events-joint, conditional, Marginal probabilities-

Probabaility distribution of a Random variable-Expected value and variance.

UNIT-IV

Theoretical probability distribution-Binomial, Normal and students t distributions.

UNIT-V

Estimation-population and sample-population parameters-Central Limit and theorem-point

estimate and interval estimates of population mean and population proportion.

Concept and Construction of Index numbers. Understanding Index numbers applicable in

the context of economics, business and Management.

OPERATIONS RESEARCH METHODS

UNIT-I

Linear Programming-Graphical Method for two-dimensional problems-General Problem of

Linear programming-Various definitions-Statements of basic theorems & properties. Phase I

and Phase II of the Simplex Method-Sensitivity analysis-transportation Problem and its

Solution. Assignment Problem and its Solution Duality and Shadow Price.

UNIT-II

Queueing theory: Characteristics of queueing Systems-Steady State M/M/1, M/M/C and

M/M/K queueing Models.

Replacement theory: Replacement of items that deteriorate-Replacement of items that fail -

Group replacement.

UNIT-III

Inventory theory: Costs involved in inventory Problems-Single item deterministic Model-

Economic lot size Models without shortages & with shortages having production rate infinite

& finite.

UNIT-IV

Decision Making:Decision under certainty, uncertainty & under risk. Decision trees-expected

value of Project information & imperfect information.

UNIT-V

PERT & CPM: Arrow networks-time estimates-earliest expected time, latest allowable

occurrence- critical path- probability of meeting scheduled time of completeness of projectscalculations

on CPM networks, various floats for structures- external path-updating projectoperation

time cost trade of curve.

ACTUARIAL STATISTICS

UNIT-I

Elements of Compound Interest (nominal and effective rates of interests). Annuities certain,

Present values, accumulated amounts, deferred annuities - Simple problems.

UNIT-II

Redemption of loans, Sinking funds, The Average yield on the life fund of an insurance

office. Simple Problems.

UNIT-III

The mortality table - construction, characteristics and uses of mortality table . The features of

Indian assured lives, Orientals 1925-1935 mortality tables. The LIC (1961-64) table and the

LIC(1970-7 table - Simple Problems

UNIT-IV

Premiums, general principles, natural premiums, level premiums, office premiums, loading

for expenses. With profit and without profit premiums, adequacy of premiums relative

consistency.

UNIT-V

Life office valuation, General principles, Policy values, Retrospective and prospective

methods of valuation of liabilities. (net premium, gross premium and bounds reserve) Sources

of surplus principle method of surplus.

DESCRIPTIVE STATISTICS

UNIT-I

Origin-Scope-Functions, limitations, uses and Misuses of statistics. Classification and

Tabulation of data, Diagrammatic and graphic representation of data.

UNIT-II

Measure of Central tendency-Measures of Dispersion-relative measures of dispersion-

Skewness and Kurtosis-Lorenz's curve.

UNIT-III

Elementary Probability space-Statistical probability Axiomatic approach to probability-

Finitely additive and countable additive probability functions-Addition and multiplication

theorems-Conditional probability-Bayes theorem-Simple problems

UNIT-IV

Random variables-Discrete and continuous random variables-Distribution function and

probability density function of a random variable-Expectation of a random variable-Addition

and product theorems- Evaluation of standard measures of location, dispersion, Skewness and

Kurtosis

UNIT-V

Simple linear correlation and regression-Regression equations-their properties spearman's

Rank correlation Co-efficient.

DATA ANALYSIS

UNIT-I

Sampling procedure - determination of Sample size and selection of sample formation of

questionnaire- Structured and unstructured questionnaire. Field work- Execution of surveydata

collection, Scaling techniques -Guttman scale-Likert 5 points scale.

UNIT-II

Summarizing data- tabulation- averages- Dispersions- measurement of risk- relative measures

of dispersion-efficiency and consistency- comparison of two or more populations-large

samples test, small sample test - ANOVA - Application of Statistical packages.

UNIT-III

Association of attributes: Chisquare test- correlation-rank difference correlation/biserial

correlation, point biserial correlation. Significance of correlation, rank correlation and

biserial correlation coefficient, partial and multiple correlations. Significance of multiple

regression equation-significance of bo, b1.. bn the liner regression coefficient- application of

statistical packages.

UNIT-IV

Non-parametric tests: Tests for randomness, Run test, Sign test, and Mann Whitney U test.

Wilcoxzon signed rank test. Median test- Statistical packages

UNIT-V

Curve fitting - Curves of type

Y=a+bx+cx2 Y= abx

Y =a+bx+cx Y=a.ebx

Time series -estimates of trend and seasonal variation -forecasting -statistical packages.

STATISTICAL METHODS FOR INDUSTRIES

UNIT-I

Historical development of Statistical Quality Control - Meaning of Quality - improvement -

Quality cost - Total Quality Management - causes of variations - X, R, P and C charts.

UNIT-II

Acceptance sampling plans by Attributes - Single Sampling Plan - Double Sampling Plan -

OC curves - AOQ, ATI curves, Dodge Roaming AOQL and LTPD plans, MIL - STD 105D

plans.

UNIT-III

Variable Sampling Plan - One sided and Two sided specifications - Taguchi philosophy and

contributions to Quality Improvement ( Basic concepts only)

UNIT-IV

Test of significance and design of experiments: Tests based on t, F and chi-square

distributions - Analysis of variance - One way and Two way classification Complete

Randomized Design(CRD), Randomized Block Design(RBD) , Latin Square Design(LSD).

UNIT-V

Basic of reliability theory - Life time distribution - Hazard rate- Survival function-

Exponential, Weibull, Gamma and life time distributions

STATISTICAL METHODS FOR RESEARCHERS

UNIT-I

Definition of Statistics and its applications in various disciplines - Collection of Data -

Classification, Tabulation and graphical representation of data- Construction of univariate

and Bivariate frequency distribution-measures of central tendency-measures of dispersion -

coefficient of variation.

UNIT-II

Random experiment-sample space-events-mathematical and statistical definition of

probability-conditional probability-Baye's theorem-random variable-distribution functionmoments-

Binomial distribution-Poisson distribution-normal distribution and their properties

UNIT-III

Scatter diagram-Karl Pearson's coefficient of correlation - concurrent deviation methodcoefficient

of determination-Spearman's Rank correlation-Linear regression-regression lines.

UNIT-IV

Tests of significance-types of hypotheses-two types of errors-critical region-level of

significance, small sample tests based on t, F distribution, Chi-square test of goodness of fit,

contingency table-test of independence of factors-Large sample tests.

UNIT-V

Test of equality of several populations means, one way and two way analysis of variance.

Non-parametric tests-sign, Run and Median tests-two sample rank test-sampling and its uses,

sampling methods- unrestricted Random sampling (SRS)- Restricted Sampling (Stratified and

Systematic).

STATISTICAL METHODS FOR BIOLOGISTS

UNIT-I

Nature of Biological and Clinical experiments of data-Classification and tabulation of data-

Diagrammatic representation of data- Histogram and frequency curves

UNIT-II

Measures of Central tendency-Mean, Median, Mode, Geometric mean, Harmonic Mean-

Measures of deviation - Range, Mean deviation, Quartile and standard deviation - Measures

of Skewness and Kurtosis.

UNIT-III

Correlation : Rank Correlation - Multiple and Partial Correlation - Regression - Regression

equations for biological problems.

UNIT-IV

Basic concepts of sampling - Simple random sample - Stratified sample - systematic sample

- cluster sample. Test of significance based on large sample - Mean, Variance and

Proportions.

UNIT-V

Analysis of variance -One way and Two way classifications - Completely Randomized

blocks - Randomized Block design and Latin Square Design (Simple problems based on

biological data)

ELEMENTS OF OPERATIONS RESEARCH

UNIT-I

Linear Programming Problem - Graphical Method - General Problem of Linear

Programming - Simplex Method - Phase I and Phase II Problems - Transportation and

Assignment Problems.

UNIT-II

Replacement theory : Replacement of Items that deteriorate - Replacement of items that fail

completely - Individual and group replacement policy.

UNIT-III

Sequencing Theory - Processing 'n' jobs through 2 machines - Processing 'n' jobs through 3

machines - Processing 'n' jobs through 'm' machines.

UNIT-IV

Network Theory - Introduction to Network - Determination and flow for Critical Path

Method - Project Evaluation Review Techniques and its differences.

UNIT-V

Inventory Theory - Meaning of Inventory - Factors involved in Inventory - Economic

Models with and without shortages