This course is a continuation of STAT 351, using the same text. We will
cover most of the remaining material from the text that was not covered in STAT 351,
plus additional material as time allows.
Multiple Random Variables: multivariate distributions;
joint probability, density, and distribution functions; marginal
distributions; independent random variables; order statistics;
multinomial distribution; transformations of n random variables;
beta, t, chi-squared, and F distributions (Chapter 9 of
text and class notes).
Expectations Involving Multiple Random Variables: expectation
of a sum of random variables; covariance and correlation; calculating
expectations by conditioning; multivariate normal distributions (Chapter 10 of text and class notes).
Limit Theorems: moment generating functions; sums of
independent random variables; markov and chebyshev inequalities;
modes of convergence; laws of large numbers; chernoff bounds and large deviations (if time);
central limit theorem (Chapter 11 of text and class notes).
Random Walks and Brownian Motion: random processes;
counting sample paths; time and spatial homogeneity; independent
increments; Markov property; first passage times; stochastic calculus;
option pricing (Section 12.5 of text and class notes).
Simulation: simulation of combinatorial problems; simulation of random variables; monte carlo methods (Chapter 13 of text and class notes).
Stationary Processes: definitions; Doob decomposition; autocovariance and spectra; stochastic integration and spectral representation; the ergodic theorem; Gaussian processes (Class notes).