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Question is attached as an image from the textbook. Let Z be the standard normal random variable. (a) Find the value of the probability density

Question is attached as an image from the textbook.

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Let Z be the standard normal random variable. (a) Find the value of the probability density function fr(x) of X = [Z + 1 for x = 1. (b) Find the value of the probability density function fy() of Y = e- fory = 2. (c) Find E[Y ] (Hint: this problem is closely related to the moment generating function for the normal distribution.)

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