M.Sc in Statistics with Compulsory Diploma in Actuarial Science

Bharathiar University
In Coimbatore

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  • Master
  • Coimbatore
Description

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.

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Venues

Where and when

Starts Location
On request
Coimbatore
Bharathiar University, Coimbatore, 641046., Tamil Nadu, India
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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

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