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# The simple Poisson process of Section 3.6 is characterized

ISBN: 9780321629111 32

## Solution for problem 120E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 120E

The simple Poisson process of Section 3.6 is characterized by a constant rate ? at which events occur per unit time. A generalization of this is to suppose that the probability of exactly one event occurring in the interval[ t,t + ?t] is ?(t). ?t + o(?t). It can then be shown that the number of events occurring during an interval [t1, t2] has a Poisson distribution with parameter The occurrence of events over time in this situation is called a nonhomogeneous Poisson process. The article “Inference Based on Retrospective Ascertainment,” J. Amer. Stat. Assoc., 1989: 360–372, considers the intensity function ?(t) = e a+bt as appropriate for events involving transmission of HIV (the AIDS virus) via blood transfusions. Suppose that a = 2 and b = .6(close to values suggested in the paper), with time in years. a.? hat is the expected number of events in the interval [0, 4]? In [2, 6]? b.? ?What is the probability that at most 15 events occur in the interval [0, .9907]?

Step-by-Step Solution:

Answer Step 1 of 4 Given (t) = e a+bt, a=2, b=0.6 2+0.6t Then (t)=e Step 2 of 4 a)The expected number of events in the interval [0, 4] t2 = (t) dt t1 4 = 2+0.6dt 0 0.6t2 4 =[e2 + 0.6t(2t + 2 ]0 =123.44 The expected number is 123

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321629111

Since the solution to 120E from 3 chapter was answered, more than 307 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 120E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The answer to “The simple Poisson process of Section 3.6 is characterized by a constant rate ? at which events occur per unit time. A generalization of this is to suppose that the probability of exactly one event occurring in the interval[ t,t + ?t] is ?(t). ?t + o(?t). It can then be shown that the number of events occurring during an interval [t1, t2] has a Poisson distribution with parameter The occurrence of events over time in this situation is called a nonhomogeneous Poisson process. The article “Inference Based on Retrospective Ascertainment,” J. Amer. Stat. Assoc., 1989: 360–372, considers the intensity function ?(t) = e a+bt as appropriate for events involving transmission of HIV (the AIDS virus) via blood transfusions. Suppose that a = 2 and b = .6(close to values suggested in the paper), with time in years. a.? hat is the expected number of events in the interval [0, 4]? In [2, 6]? b.? ?What is the probability that at most 15 events occur in the interval [0, .9907]?” is broken down into a number of easy to follow steps, and 170 words. This full solution covers the following key subjects: Events, interval, Poisson, occurring, suppose. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9.

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