Problem 4. Antonio runs a shoe repair store by himself. Customers arrive to bring a pair of shoes to be repaired according to a Poisson process at a mean rate of 1 per hour. The time Antonio requires to repair each individual shoe has an exponential distribution with a mean of 15 minutes.

(a) Calculate the expected number of pairs of shoes in the shop.

(b) Calculate the expected amount of time from when a customer drops off a pair of shoes until they are repaired and ready to be picked up.