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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.
- Spring '10
- The Land