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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 denote a random sample of size 3 from a gamma

Chapter 5, Problem 7E

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QUESTION:

Problem 7E

Let X1,X2,X3 denote a random sample of size 3 from a gamma distribution with α = 7 and θ = 5.

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

(b) How is Y distributed?

Questions & Answers

QUESTION:

Problem 7E

Let X1,X2,X3 denote a random sample of size 3 from a gamma distribution with α = 7 and θ = 5.

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

(b) How is Y distributed?

ANSWER:

Problem 7E

Let  denote a random sample of size 3 from gamma distribution with and

(a) Find the mgf  of  .

(b) How is Y distributed?

                                                              Step by Step Solution

Step 1 of 2

Given that , denote a random sample of size 3 from gamma distribution with and .

It is known that the moment generating function (MGF) of gamma distribution with parameters and  is

                      (i)

Putting the values of  and  in equation (i),

The MGF of  is

So, MGF of is

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