MA61036: Probability Theory

MA61036
Course name	Probability Theory
Offered by	Mathematics
Credits	4
L-T-P	3-1-0
Previous Year Grade Distribution
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Semester	{{{semester}}}

Syllabus

Syllabus mentioned in ERP

Prerequisite: voidClassical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, Bayes Theorem and independence. Discrete, continuous and mixed random variables, probability mass, probability density and cumulative distribution functions, mathematical expectation, moments, moment generating function, Special distributions- discrete uniform, binomial, geometric, negative binomial, hypergeometric, Poisson, continuous uniform, exponential, gamma, Weibull, Pareto, beta, normal, lognormal, inverse gaussian, Cauchy, double exponential distributions. Functions of a random variable. Joint distributions, product moments, independence of random variables, bivariate normal distribution, transformations of random variables. Sampling Distributions - distributions of the sample mean and the sample variance for a normal population, Chi-Square, t and F distributions, distributions of order statistics. Moment inequalities - Chebychev, Markov, Liapunov, Holder, Cr, Basic, Minkowski, Cauchy-Schwartz, Kolmogorov, Jensen. Convergence of random variables â convergence in probability, convergence almost surely, convergence in rth mean, convergence in distribution â their interrelationships. Characterstic functions, inversion and continuity theorems. Zero-One Laws, Weak and strong laws of large numbers and their properties. Central Limit Theorems â Lindberg-Levy, Liapunov and Lindberg-Feller.