4. Wackerly 3.158 If Y is a random variable with moment-generating function m(t) and if W is given by WaY+b, show that the moment-generating function of W is ebm (at).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Number 4

Revision: Moment-generating Functions
4. Wackerly
3.158 If Y is a random variable with moment-generating function m(t) and if W is given by
W = aY+b, show that the moment-generating function of W is ebm (at).
5. Wackerly
4.137 Show that the result given in Exercise 3.158 also holds for continuous random variables. That
is, show that, if Y is a random variable with moment-generating function m(t) and U is given
by UaY+b, the moment-generating function of U is ebm(at). If Y has mean and
variance o², use the moment-generating function of U to derive the mean and variance of U.
Transcribed Image Text:Revision: Moment-generating Functions 4. Wackerly 3.158 If Y is a random variable with moment-generating function m(t) and if W is given by W = aY+b, show that the moment-generating function of W is ebm (at). 5. Wackerly 4.137 Show that the result given in Exercise 3.158 also holds for continuous random variables. That is, show that, if Y is a random variable with moment-generating function m(t) and U is given by UaY+b, the moment-generating function of U is ebm(at). If Y has mean and variance o², use the moment-generating function of U to derive the mean and variance of U.
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