Establish the result in Example 41 concerning the difference of two independent normal random variables, \(X\) and \(Y\).

Data From Example 41

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EXAMPLE 41 Sum of two independent normal random variables is normal Let X and Y be independent normal random variables. Let X have mean x and vari- ance of while Y has mean y and variance of. Use moment generating functions to show that (a) X + Y has a normal distribution with mean x + y and variance +0. (b) XY has a normal distribution with mean x +0. - and variance