(a) Find the moment generating function of U = X +3Y+Z. State clearly and justify all steps taken. (b) Calculate the expectation E(U) using the moment generating function.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
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Suppose that X, Y and Z are statistically independent
random variables, each of them with a x²(2) distribution.
(a) Find the moment generating function of U = X + 3Y + Z. State clearly and
justify all steps taken.
(b) Calculate the expectation E(U) using the moment generating function.
Hint: You may use without proof the fact that the moment generating function of a
x²(v) random variable W is
v/2
Mw(t) =
- 2t
Transcribed Image Text:Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2) distribution. (a) Find the moment generating function of U = X + 3Y + Z. State clearly and justify all steps taken. (b) Calculate the expectation E(U) using the moment generating function. Hint: You may use without proof the fact that the moment generating function of a x²(v) random variable W is v/2 Mw(t) = - 2t
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