MSc (Mathematics and Computing) Programme:Probability and Statistics

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.