Homework SourseLet X be a standard normal random variable and Y eX a Obtai
Let X be a standard normal random variable and Y = e^X,
(a) Obtain E[sin(2?X)].
(b) Obtain the PDF of Y .
(c) Using the MGFof X,obtain the nth moment of Y, n=1,2,....
(d) Let Z be a continuous random variable with PDF
Using (a), obtain c and the nth moment of Z.
(e) What conclusion can you draw?
1+sin(2r Ing g(y) = cySolution
![Let X be a standard normal random variable and Y = e^X, (a) Obtain E[sin(2?X)]. (b) Obtain the PDF of Y . (c) Using the MGFof X,obtain the nth moment of Y, n=1,](/WebImages/7/let-x-be-a-standard-normal-random-variable-and-y-ex-a-obtai-993171-1761510937-0.webp "Let X be a standard normal random variable and Y = e^X, (a) Obtain E[sin(2?X)]. (b) Obtain the PDF of Y . (c) Using the MGFof X,obtain the nth moment of Y, n=1,")
