Advanced Statistics with Applications in R

Chapter 2Continuous random variables

Unlike discrete random variables, continuous random variables may take any value on a specified interval. Usually, we deal with continuous random variables that take any value on an infinite or semi‐infinite interval, denoted as or respectively. Some continuous random variables, such as uniform or beta‐distributed random variables, belong to an interval. A characteristic property of a continuous random variable is that for any value Although it is possible that a random variable is a combination of a discrete and a continuous variable, we ignore this possibility. Thus, only continuous random variables are considered in this chapter, with calculus as the major mathematical tool for investigating of distributions of these variables. Regarding the notation, typically, random variables are denoted as uppercase, like and the values it takes or the argument of the density function as lowercase, . This notation rule will be followed throughout the book. ...