4106-08-h5 - HMWK 5 Problems from the Text Ch. 6, Page 409:...

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HMWK 5 Problems from the Text Ch. 6, Page 409: 12, 13, 22 Problems not from the textbook 1. According to a Poisson process at rate λ = 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. (a) Compute the expected number of units held at times t = 20, t = 50 and t = 90 days. (b) What is the long-run average number of units held by the company? (c) Repeat (a), (b) when H has a uniform distribution on (40 , 80). 2. Printer with jams : Jobs arrive to a computer printer according to a Poisson process at rate λ . Jobs are printed one at a time requiring iid printing times that are exponentially distributed with rate μ . Jobs wait in a FIFO queue before entering service. Additionally, independently, the printer jams at times that form a Poisson process at rate γ . Whenever a jam ocurrs the job being printed (if any) is removed, and the printer
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