Q33, page 326, Introduction to probability, Joseph K.Blitzstein. Please solve the problem:Alice walk

Q33, page 326, Introduction to probability, Joseph K.Blitzstein. Please solve the problem:Alice walks into a post office with 2 clerks. Both clerks are in the midst of servingcustomers, but Alice is next in line. The clerk on the left takes an Expo(?1) time toserve a customer, and the clerk on the right takes an Expo(?2) 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.