BIOSTATS 6003EX - Probability and Distribution Theory

This course will focus on applying the calculus-based techniques learned in Mathematical Background for Biostatistics to the study of probability and statistical distributions. These two courses, together with the subsequent Principles of Statistical Inference course, will provide the core prerequisite mathematical statistics background required for the study of later courses in the Graduate Diploma or Masters degree. This course begins with the study of probability, random variables, discrete and continuous distributions, and the use of calculus to obtain expressions for parameters of these distributions such as the mean and variance. Joint distributions for multiple random variables are introduced together with the important concepts of independence, correlation and covariance, marginal and conditional distributions. Techniques for determining distributions of transformations of random variables are discussed. The concept of the sampling distribution and standard error of an estimator of a parameter is presented, together with key properties of estimators. Large sample results concerning the properties of estimators are presented with emphasis on the central role of the normal distribution in these results. General approaches to obtaining estimators of parameters are introduced. Numerical simulation and graphing with Stata is used throughout to demonstrate concepts.