At times that form a Poisson process at rate= 25 (per hour),people rent a Citibike, and independently they use it for a random amount of timedistributed as continuous Uniform(0,8) (hours) then return it. Assume initially, attimet= 0, there were no Citibikes rented out, and also assume that there are anunlimited number of Citibikes.YOU MUST SHOW YOUR WORK.

(a) What is the expected number of Citibikes rented out at timet= 2?

(b) What is the long-run average number of Citibikes rented out?

(c) LetK(9) = the number of Citibikes rented out at timet= 9.Derive explicitlythe probabilitiesP(K(9) =j), j0