Question: Let Z be a standard normal random variable. (a) Calculate the moment-generating function of Z. (b) Use part (a) to find the moment-generating function of

Let Z be a standard normal random variable.

(a) Calculate the moment-generating function of Z.

(b) Use part

(a) to find the moment-generating function of X, where X is a normal random variable with mean μ and variance σ2.

(c) Use part

(b) to calculate the mean and the variance of X.

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