Probability Models and Distribution Functions

The chapter provides the basics of probability theory and of the theory of distribution functions, and discusses the probability model for random sampling. It discusses several families of discrete distributions such as binomial distribution and hypergeometric distribution, and illustrates their possible application in modeling industrial phenomena. The chapter deals with continuous distributions, under which uniform distribution, normal and log-normal distributions, exponential distribution, gamma and Weibull distributions, and Beta distributions, are dealt with. Later, joint, marginal and conditional distributions, and multivariate distributions, are explained. The law of large numbers (LLN) and central limit theorem (CLT) are also explained in the chapter. Controlled Vocabulary Terms Bayes’ theorem; central limit theorem; continuous distributions; discrete distributions; joint probability distribution; marginal distribution; multivariate statistics; Random variables