The two random variables in Exercise 11.6 are special cases of Gam(α, λ) variables, namely with α = 2 and λ = 1/2. More generally, let X1,...,Xn be independent Gam(k, λ) distributed random variables,...

The two random variables in Exercise 11.6 are special cases of Gam(α, λ) variables, namely with α = 2 and λ = 1/2. More generally, let X1,...,Xn be independent Gam(k, λ) distributed random variables, where λ > 0 and k is a positive integer. Argue—without doing any calculations— that X1 + ··· + Xn has a Gam(nk, λ) distribution