Use your answer from 3.87 to show that E(Y) = aE(X) +b
3.87: [ If X is a random variable with moment-generating function M(t), and Y is a function of X given by Y=aX+b,
show that the moment-generating function for Y is e^(tb) * M(at) ]
My answer for exercise 3.87 is attached.
The solution shows how to find the expected value of Y using its moment generating function.