In hypothesis testing (HT), we generally assume the underlying distribution is normal (with reasonable arguments). But as we discussed before, there are many other impor- tant distributions in practice. Here we will study HT for other distributions, and we take the exponential distribution as an example, recall that exponential distributions are often used to model lifetimes.

(a) For i.i.d. RVs X1, X2, X, Exp(A) with size n, denote S, X+X++ X show that X2XS~ X2n Hint: Consider the MGF approach, also the fact that the MGF of XI(a, b) is M(t) = (1 - beta*t) ^ (- alpha) for t < 1/beta can be helpful.