MSc (Mathematics and Computing) Programme:Probability and StatisticsThapar University
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Real Analysis – I
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Based Management Systems
Computer Based Optimization Techniques
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.