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To introduce students to Probability Theory.
Axioms of probability, Conditional probability and independence, Discrete random variables: bernouilli, binomial, poisson, geometric, hypergeometric. Expectation; mean and variance. Continuous random variables: exponential, gamma, normal. Transformations. Joint distributions, marginal distributions and conditional distributions. Sums, order statistics. Multinomial. Bivariate normal. Expectation of functions, linear combinations. Covariance and correlation. Moment generating function. Limit theorems: inequalities, law of large numbers, central limit theorem, approximation. Sampling distributions: F and chi-squared.