Unformatted text preview: tation to compute E (T T < c). (b) Determine E (T T < c)
from the identity
ET = P (T < c)E (T T < c) + P (T > c)E (T T > c)
2.33. When did the chicken cross the road? Suppose that tra c on a road
follows a Poisson process with rate cars per minute. A chicken needs a gap of
length at least c minutes in the tra c to cross the road. To compute the time
the chicken will have to wait to cross the road, let t1 , t2 , t3 , . . . be the interarrival 96 CHAPTER 2. POISSON PROCESSES times for the cars and let J = min{j : tj > c}. If Tn = t1 + · · · + tn , then the
chicken will start to cross the road at time TJ 1 and complete his journey at
time TJ 1 + c. Use the previous exercise to show E (TJ 1 + c) = (e c 1)/ .
Random sums
2.34. Edwin catches trout at times of a Poisson process with rate 3 per hour.
Suppose that the trout weigh an average of 4 pounds with a standard deviation
of 2 pounds. Find the mean and standard deviation of the total weight of ﬁsh
he catches in two hours.
2.35. An insurance company pays out...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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