MATH 7550 Probability and Statistics I

Various types of convergence, independent incraments, stable laws, central limit problem. Central limit theorems, x^2 distribution, contingency tables. Sampling distributions for normal populations (t, x^2, F). Estimation of parameters: minimum variance, maximum likelihood, sufficiency, nonparametric estimation. Hypothesis testing: Neyman-Pearson lemmas, general linear models, analysis of variances and covariance, regression. Introduction to time series, sampling design, and Bayesian theory.