"Gaussian distributions, I" A. Fomenko. 1984. India ink and pencil on paper, 44 x 62 cm.
A graduate level course in probability with an emphasis on how the theory is applied in statistics, for example to construct statistical models (the important roles of independence, multivariate random variables, and stochastic processes), and to invert them (illustrative Monte Carlo applications). We will cover a range of topics mainly from a user's point of view: convergence theorems, characteristic functions, conditioning, Poisson processes, Markov chains, and martingales.
Ideally, one upper division undergraduate course in probability, and one in analysis. Co-requisite: STAT 460 / 560 or equivalent. If you are unsure, contact me by email with your (unofficial) graduate and undergraduate transcripts attached.
[G+S] G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes, 3rd edition, Oxford, (2001). There is a solutions manual to this text: G.R. Grimmett and D.R. Stirzaker, One Thousand Exercises in Probability, Oxford, (2001).