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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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Let X1, X2, X3 be mutually independent random variables

Chapter 5, Problem 3E

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QUESTION:

Problem 3E

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).

Questions & Answers

QUESTION:

Problem 3E

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).

ANSWER:

Problem 3E

Let  be mutually independent random variables with Poisson distribution having means 2, 1 and 4 respectively.

(a). Find the mgf of the sum .

(b). How is Y distributed?

(c). Compute P(3  Y  9).

                                                              Step by Step Solution

Step 1 of 3

The MGF of Poisson distribution with parameter is

Given that be mutually independent random variables with Poisson distribution having means 2, 1 and 4 respectively. Therefore,

Then, the MGF of  is

So, the MGF of  is

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