Orientation. Combinatorial probability. Fluctuations in Coin Tossing and Random Walks.Combination of Events, Occupancy and Matching Problems. Conditional probabilities. Urn Models. Independence.
Random Variables, discrete distributions, Expectation, variance and moments, probability generating functions and moment generating functions, Tchebychevs inequality. Standard discrete distributions: uniform, binomial, Poisson, geometric, hypergeometric, negative binomial.
Continuous 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 vari-ables.
Laws of Large Numbers and Central Limit Theorem (Proofs optional)
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