(a) Let S and T be independent exponential A random variables. Find the joint distri- bution of S/(S + T) and S + 7. Give an interpretation of this result in terms of Poisson processes. (b) Let R and U be independent random variables having respectively, a uniform distri- bution over 0, 1] and a gamma distribution with parameters 2 and A. Deduce from (a) that RU and (1 - R)U are independent exponential A random variables. (c) Let U be a gamma random variable with parameters o and A, and let a > 1-Q. Obtain E[(*-]]. (d) Use (b) and (c) to obtain the identity: '0