Solution Found!
Let Y1 and Y2 be independent random variables with
Chapter 6, Problem 38E(choose chapter or problem)
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).
Questions & Answers
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 .