29. A group of skiers continually, and independently, climb up and then ski down a particular...

29. A group of ç skiers continually, and independently, climb up and then ski down a particular slope. The time it takes skier / to climb up has distribution Fi9 and it is independent of her time to ski down, which has distribution Hi9 i = 1, ...,n. Let N(t) denote the total number of times members of this group have skied down the slope by time Also, let U(t)

denote the number of skiers climbing up the hill at time t.

(a) Whatislimf_,eA/iO/f?

(b) Find ]img^P[U(t) = k}.

(c) If all Ft are exponential with rate ë and all Gf are exponential with rate ì, what is P[U(t) = k]l