57. a. Show that if X has a normal distribution with parameters and , then Y ...

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57.

a. Show that if X has a normal distribution with parameters and , then Y aX b (a linear function of X)

also has a normal distribution. What are the parameters of the distribution of Y [i.e., E(Y) and V(Y)]? [Hint:

Write the cdf of Y, P(Y y), as an integral involving the pdf of X, and then differentiate with respect to y to get the pdf of Y.]

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