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# Let Y1 and Y2 be independent random variables with

ISBN: 9780495110811 47

## Solution for problem 38E Chapter 6

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition

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Problem 38E

Problem 38E

Let Y1 and Y2 be independent random variables with moment-generating functions mY1 (t) and mY2 (t), respectively. If a1 and a2 are constants, and U = a1Y1 + a2Y2 show that the moment-generating function for U is mU (t) = mY1 (a1t) × mY2 (a2t).

Step-by-Step Solution:

Solution:

Step 1 of 2:

Let Y1 and Y2 be independent random variables with moment- generating functions and respectively.

Let  a1 and a2 are constants, and U= a1 Y1+ a2 Y2.

We have to show that the moment-generating function for U is .

Step 2 of 2

##### ISBN: 9780495110811

The answer to “Let Y1 and Y2 be independent random variables with moment-generating functions mY1 (t) and mY2 (t), respectively. If a1 and a2 are constants, and U = a1Y1 + a2Y2 show that the moment-generating function for U is mU (t) = mY1 (a1t) × mY2 (a2t).” is broken down into a number of easy to follow steps, and 45 words. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This full solution covers the following key subjects: generating, moment, let, constants, independent. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The full step-by-step solution to problem: 38E from chapter: 6 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. Since the solution to 38E from 6 chapter was answered, more than 555 students have viewed the full step-by-step answer. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811.

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Let Y1 and Y2 be independent random variables with