Alice walks into a post office with 2 clerks. Both clerks are in the midst of serving customers, but Alice is next in line. The clerk on the left takes an Expo(λ1) time to

serve a customer, and the clerk on the right takes an Expo(λ2) time to serve a customer. Let T be the amount of time Alice has to wait until it is her turn.

(a) Write down expressions for the mean and variance of T, in terms of double integrals

(which you do not need to evaluate).

(b) Find the distribution, mean, and variance of T, without using calculus.