According to a Poisson process at rate 20 per day, a company buys units (100 share blocks) of stock A and holds on to each unit, independently of other units, for H days, where H has an exponential distribution with E(H) = 60 (days).

Assume that initially (time t = 0) no units of stock A are held.

1) For the uniform distribution (40, 80) for H, compute the probability that at time t = 5 there are 0 units held by the company. Repeat for the case when H has an exponential distribution with E(H) = 60 (days).

2) Compute the expected number of units held at times t = 20, t = 50 and t = 90 days and the long-run time-average number of units held by the company when H is constant at size 60 days: P(H = 60) = 1.

Please explain the answers.