Stochastic

# He wants to leave early but he does not want to lose

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Unformatted text preview: u play 20 hands of poker. 2.21. Suppose 1% of a certain brand of Christmas lights is defective. Use the Poisson approximation to compute the probability that in a box of 25 there will be at most one defective bulb. Poisson processes: Basic properties 2.22. Suppose N (t) is a Poisson process with rate 3. Let Tn denote the time of the nth arrival. Find (a) E (T12 ), (b) E (T12 |N (2) = 5), (c) E (N (5)|N (2) = 5). 2.23. Customers arrive at a shipping o ce at times of a Poisson process with rate 3 per hour. (a) The o ce was supposed to open at 8AM but the clerk Oscar overslept and came in at 10AM. What is the probability that no customers came in the two-hour period? (b) What is the distribution of the amount of time Oscar has to wait until his ﬁrst customer arrives? 2.24. Suppose that the number of calls per hour to an answering service follows a Poisson process with rate 4. (a) What is the probability that fewer (i.e., <) than 2 calls came in the ﬁrst hour? (b) Suppose that 6 calls...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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