Let Y1 and Y2 be independent random variables with

Chapter 6, Problem 38E

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QUESTION:

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).

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QUESTION:

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).

ANSWER:

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 .


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