Random Variables: The Continuous Case

This chapter considers variables which take values in an interval. Historically the continuous random variables appeared as approximations of the discrete random variables. A crucial notion in the theory of continuous random variables is the concept of probability density function. A section provides examples of density functions. The chapter goes on to provide illustrations of the cumulative distribution function (c.d.f.) of a continuous random variable, and explains properties of the c.d.f. of the continuous random variables. Moments for several classical random variables are presented. The following question is discussed: How do you find the density of a random variable Y constructed as a function h(X ), where X is a random variable with a given density function? Finally, the chapter presents some of most used continuous probability distributions and discusses their basic properties.