Probability Theory and Mathematical Statistics - KFUPM

Combinatorial methods, classical models of probability. Set functions. Axiomatic definition of probability. Conditional probability and Bayes' theorem. Random variables and their types. Distributions, moments, moment generating functions, cumulative distribution function. Hazard function with applications. Covariance and correlation. Special discrete and continuous distributions. Random vectors and their distributions. Marginal and conditional distributions. Independent random variables. Functions of random variables. Sums of independent random variables. Chebyshev's inequality, weak law of large numbers and the central limit theorem.