3.158 If Y is a random variable with moment-generating function m(t) and if W is given by W = aY + b, show that the moment-generating function of W is e¹¹ m(at). 3.159 Use the result in Exercise 3.158 to prove that, if W = aY+b, then E(W) = aE(Y) + b and V(W) = a²V (Y).

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