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.
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;
gamma, beta, and chi-squared distributions (Chapter 9 of
text and lectures).
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 lectures).
Limit Theorems: moment generating functions; sums of
independent random variables; markov and chebyshev inequalities;
modes of convergence; laws of large numbers; chernoff bounds;
central limit theorem (Chapter 11 of text and lectures).