Functions of Random Variables

This chapter discusses single random variables and its transforms. Various types of transformations such as sum, squares, square-roots, absolute-value, reciprocals, transcendental and arbitrary functions are discussed and illustrated with numerous examples. Distribution of minimum and maximum, integer and fractional parts, sum of squares of IID RVs as well as the distribution of CDF and its inverse are also described. A summary table of transformations is provided to find the transformed densities easily. These results are used to express the mean deviation of continuous random variables as a simple integral from lower limit to F(mean) where F() is the CDF. This chapter ends with a discussion of applications of functions of random variables in various fields.