10 of the vehicles are trucks the other 90 are cars a

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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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