Probability And Mathematical Statistics I

Catalog description

Intended for advanced undergraduates and beginning graduate students in the mathematicalsciences, and for others intending to pursue the mathematical study of probability and statistics.Topics covered include axiomatic foundations, the calculus of probability, conditional probability andindependence, Bayes’ Theorem, random variables, discrete and continuous distributions, joint, marginal and conditional distributions, covariance and correlation, expectation, generating functions, exponential families, transformations of random variables, types of convergence, laws of large numbers the Central Limit Theorem, Taylor series expansion, the delta method. (Prerequisite: knowledge of basic probability at the level of MA 2631 and of advanced calculus at the level of MA 3831/3832 is assumed.)