Question: 2. Let X be a random variable with moment generating function My (r) and let Y = ax +b, where a and b are constants.

2. Let X be a random variable with moment generating function My (r) and let Y = ax +b, where a and b are constants. Then My(r) =e My (ar ) (you do not have to prove this fact). (a) Use the moment generating function to prove that E(Y) = b + aE(X ). [4 Marks] (b) Now let My (r) = est and let Y = (X -3)/4. Find My(r) and use it to find the expectation E (Y) and the variance V (Y). [6 Marks]

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