1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that of a random variable Y is MY(t)=((4/5)e^t+1/5)^16. If X and Y are independent, find each of the following. (a) P{X+Y=2}= (b) P{XY=0}= (c) E[XY]= (d) E[(X+Y)^2]=
1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that of a random variable Y is MY(t)=((4/5)e^t+1/5)^16. If X and Y are independent, find each of the following. (a) P{X+Y=2}= (b) P{XY=0}= (c) E[XY]= (d) E[(X+Y)^2]=
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 62E
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1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that of a random variable Y is MY(t)=((4/5)e^t+1/5)^16. If X and Y are independent, find each of the following.
(a)
P{X+Y=2}=
(b)
P{XY=0}=
(c)
E[XY]=
(d)
E[(X+Y)^2]=
———
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