et Z be the standard normal random variable. a) Find the value of the probability density function fx(x) of X = |Z+1| for x = 1. b) Find the value of the probability density function fy(v) of Y = e² for y = 2. c) Find E[Y4] (Hint: this problem is closely related to the moment generating function for the normal distribution.)

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let Z be the standard normal random variable.
(a) Find the value of the probability density function fx(x) of X = |Z+1| for x = 1.
= 2.
(b) Find the value of the probability density function fy(v) of Y = e² for y
(c) Find E[Y4] (Hint: this problem is closely related to the moment generating function for the normal
distribution.)
Transcribed Image Text:Let Z be the standard normal random variable. (a) Find the value of the probability density function fx(x) of X = |Z+1| for x = 1. = 2. (b) Find the value of the probability density function fy(v) of Y = e² for y (c) Find E[Y4] (Hint: this problem is closely related to the moment generating function for the normal distribution.)
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