Chapter 21: Transformation of Continuous Random Variables, Using the CDF Method

Suppose Y is a continuous random variable with known density fY (y) and cumulative distribution function (CDF) FY (y), and g is a function whose domain contains the support of Y. We are interested in the random variable X = g(Y). We know how to compute E(X), but we often want more information than the first moment of the new random variable. In this chapter we will use the CDF method to find the distribution of a random variable X that is a function of a continuous random variable Y. We can do this by finding the CDF FX (x) using the known CDF FY(y), then taking the derivative with respect to x to get the density.