Suppose X is a Gaussian random variable with mean
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![](https://test.transtutors.com/qimg/357877e7-eb0c-46ef-8072-7c98b9ce7b07.png)