36. Each of n skiers continually, and independently, climbs up and then skis down a particular slope. The time it takes skier i to climb up has distributionI mage, and it is independent of her time to ski down, which has distributionI mage. Let denote the total number of times members of this group have skied down the slope by time t. Also, letI mage denote the number of skiers climbing up the hill at time t.

(a) What is ?

(b) Find Image.

(c) If all Image are exponential with rate λ and all Image are exponential with rate μ, what is Image?