Fundamentals of Probability and Statistical Inference

The goal of this 3-credit course is to introduce fundamentals of probability theory, statistical inference tools and their application to biostatistics. The course is intended for first-year graduate students in Biostatistics MS program. The topics in this course include basic concepts of probability, random variables, important probability distributions (e.g., normal, exponential, binomial and Poisson), marginal distribution, conditional distribution, joint distribution, expectation and variance, conditional expectation, law of large numbers, central limit theorem, sampling distributions, point estimation, maximum likelihood estimation, method of moments and estimating equations, interval estimation, hypothesis testing. Examples from biostatistical applications will be used whenever possible. Simple simulations with R software will be used to illustrate some concepts in probability and statistical inference.