1. Suppose Y has a Γ(α, β) distribution. Let 
. Show that the pdf of X is given by expression (3.7.5). Determine the cdf of X in terms of the cdf of a Γ-distribution. Derive the mean and variance of X.
2. Write R functions for the pdf and cdf of the random variable in Exercise 3.7.1.
Exercise 3.7.1
Suppose Y has a Γ(α, β) distribution. Let . Show that the pdf of X is given by expression (3.7.5). Determine the cdf of X in terms of the cdf of a Γ-distribution. Derive the mean and variance of X.