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Unformatted text preview: HMWK 4 Problems from the Text Ch. 5, Page 346: 4, 37, 44 (Hint: Wald’s Equation) Problems not from the textbook 1. Downtown Express trains arrive to West 96th Street station according to a Poisson process at rate 4 per hour, and independent of this, Downtown Local trains arrive according to a Poisson process at rate 7 per hour. Suppose you arrive at the station (to go Downtown) and decide to take the first train that arrives. (a) What is the probability that you take an Express train? (b) What is the expected amount of time you wait for a train to arrive? (c) Given that you took an Express train (it arrived first), what was the expected amount of time you waited for it to arrive? (d) What is the probability that no trains (of any type) arrive during the next 12 min- utes? (e) Let t 3 denote the time at which the third train arrives (regardless of type). What is the variance, V ar ( t 3 ) ?...
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- Fall '08
- Operations Research, Probability theory, Poisson process, Train station, Trains, Limited-stop