# MSc (Mathematics and Computing) Programme:Probability and Statistics

Thapar UniversityPrice on request

Price on request

£ 295 - (Rs 24,591)

+ VAT

Free

£ 359 - (Rs 29,927)

## Important information

- Master
- Patiala

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

On request |
PatialaThapar University P.O Box 32, 147004, Punjab, India See map |

## Course programme

Semester I

Real Analysis – I

Linear Algebra

Complex Analysis

Fundamentals of Computer Science and C Programming

Discrete Mathematical Structure

Differential Equations

Semester II

Real Analysis –II

Advanced Abstract Algebra

Computer Oriented Numerical Methods

Data Structures

Data Based Management Systems

Operating Systems

Semester III

Topology

Computer Based Optimization Techniques

Computer Networks

Mechanics

Seminar

Semester IV

Functional Analysis

Dissertation

Probability and Statistics

Introduction: Review of axiomatic approach to probability.

Random variables: probability distribution of a random variable; Distribution function; Discrete and continuous random variables; Functions of a random variable.

Mathematical Expectation: moments, moment generating functions, Characteristic function.

Study of special distributions: binomial, Poisson, negative binomial, geometric distribution, uniform, exponential, normal, gamma, log-normal.

Bi-variate probability distribution: Marginal and conditional distributions, Bi-variate normal distribution.

Limit theorems: Modes of convergence and their interrelationships; law of large numbers, central limit theorem.

Correlation and Regression: Regression between two variables, Karl-Pearson correlation coefficient and Rank Correlation. Multiple regression, partial and multiple correlation( three variables case only)

Random Sampling: Sampling distributions of chi-square, t and F distribution of mean and variation in sampling from a normal population.

Point estimation: Problem, Probabilities of point estimates. Method of maximum likelihood.

Testing of Hypothesis: Fundamental notions, Neyman-Pearson lemma (without proof). Important tests based on normal, chi-square, t and F distributions.

Interval Estimation: Confidence interval for mean and variance.