Orientation. Combinatorial probability. Fluctuations in Coin Tossing
and Random Walks.Combination of Events, Occupancy and Matching Problems.
Conditional probabilities. UrnModels. Independence.
Random Variables, discrete distributions, Expectation, variance and
moments, probability gen-erating functions and moment generating
functions, Tchebychevs inequality. Standard discretedistributions:
uniform, binomial,
Poisson, geometric, hypergeometric, negative binomial. Con-tinuous
random variables: univariate densities and distributions, Expectations,
variance andmoments, standard univariate densities: normal, exponential,
gamma, beta,
chi-square, Cauchy.
Joint and conditional distributions, Independence of random variables, Transformation of variables.
Laws of Large Numbers (proofs optional).
Suggested Texts :
1. S. Ross, First course in probability theory, Mac Millan (1989).
2. P.G. Hoel, S.C. Port and C.J. Stone, Introduction to Probability Theory, Universal BookStall, New Delhi (1991).
3. W.Feller, An introduction to probability theory and its applications Vol 1, Wiley (1950).
4. K.L. Chung, Elementary Probability Theory, Springer (Indian reprint 2003).
- Teacher: Siva Athreya