Probability spaces, events, axioms of probability. Combinatorics, dependent and independent events, conditional probability, Bayes' theorem. Random variables - continuous and discrete. Distribution functions and density functions. Expectation, variance and higher moments. Classical probability distributions. Chebyshev's inequality. Sums of independent random variables, the weak law of large numbers and an application to Weierstrass' approximation theorem. Random vectors, conditional expectation and the curve of regression. Generating functions. The central limit theorem. Random walks.

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