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# Generalize Exercise 5.4-3 by showing that the sum of n ISBN: 9780321923271 41

## Solution for problem 4E Chapter 5.4

Probability and Statistical Inference | 9th Edition

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Problem 4E

Problem 4E

Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means μ1,μ2, . . . ,μn is Poisson with mean References Exercise 5.4-3

Let X1, X2, X3 be mutually independent random variables with Poisson distributions having means 2, 1, and 4, respectively.

(a) Find the mgf of the sum Y = X1 + X2 + X3.

(b) How is Y distributed?

(c) Compute P(3 ≤ Y ≤ 9).

Step-by-Step Solution:

Problem 4E

Generalize exercise 5.4.3 by showing that the sum of n independent Poisson random variables with respective means is Poisson with mean Step by Step Solution

Step 1 of 2

The MGF of Poisson distribution with parameter is Let be mutually independent random variables with Poisson distribution having means respectively.

Then, the MGF of is Step 2 of 2

##### ISBN: 9780321923271

Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The full step-by-step solution to problem: 4E from chapter: 5.4 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means ?1,?2, . . . ,?n is Poisson with mean References Exercise 5.4-3Let X1, X2, X3 be mutually independent random variables with Poisson distributions having means 2, 1, and 4, respectively.(a) Find the mgf of the sum Y = X1 + X2 + X3.(b) How is Y distributed?(c) Compute P(3 ? Y ? 9).” is broken down into a number of easy to follow steps, and 70 words. This full solution covers the following key subjects: Poisson, random, exercise, sum, variables. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Since the solution to 4E from 5.4 chapter was answered, more than 500 students have viewed the full step-by-step answer.

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Generalize Exercise 5.4-3 by showing that the sum of n