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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

Ask a homework question - tutors are online