Continuous Random Variables and Probability Distributions

Abstract

As mentioned at the beginning of Chapter 3, the two important types of random variables are discrete and continuous. In this chapter, we study the second general type of random variable that arises in many applied problems. Sections 4.1 and 4.2 present the basic definitions and properties of continuous random variables, their probability distributions, and their moment generating functions. In Section 4.3, we study in detail the normal random variable and distribution, unquestionably the most important and useful in probability and statistics. Sections 4.4 and 4.5 discuss some other continuous distributions that are often used in applied work. In Section 4.6, we introduce a method for assessing whether given sample data is consistent with a specified distribution. Section 4.7 discusses methods for finding the distribution of a transformed random variable.KeywordsContinuous Random VariablesSample PercentilesNormal Probability PlotStandard Beta DistributionWeibull DistributionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.