Question: Suppose X is a Gaussian random variable with mean X and variance 2x . Suppose we form a new random variable according to Y=

Suppose X is a Gaussian random variable with mean µ X and variance σ2x . Suppose we form a new random variable according to Y= aX+ b for constants a and b.
(a) Prove that Y is also Gaussian for any a ≠ 0.
(b) What values for the constants a and b will lead to the new random variable Y having zero mean and unit variance?
(c) What values for the constants a and b will lead to the new random variable Y having a mean of µY and a variance of s Yσ2?

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