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Problem 8 Show that normality is preserved by linear transformation, i.e., if X is a normal random variable with mean ,u and variance a2, and

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Problem 8 Show that normality is preserved by linear transformation, i.e., if X is a normal random variable with mean ,u and variance a2, and if a 31$ 0 and b are scalars, the random variable Y:aX+b is also normal, with mean and variance given by E[Y] : all + b and VaT(X) : (1202

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