Probability theory II 1000-115aRP2a

Convergence of probability distributions. The characteristic function of
a probability distribution, applications to computing moments and
distributions of sums of independent random variables. The uniqueness
theorem. Levy's theorem stating that the convergence of
probability distributions can be described in terms of the pointwise
convergence of their characteristic functions. The Central Limit Theorem.
Introduction to the theory of martingales ("fair games"). Stopping
moments. Doob's "optional sampling" theorem. Markov chains, ergodicity.