Question: How to take expectation of function of random variable


I have a random variable that follows Uniform(1,4). Now I have a function which is of the following type:

g := a*alpha+b*t/alpha+exp(alpha)


A := RandomVariable(Uniform(c, d));
                 RandomVariable(Uniform(c, d))
f := proc (alpha) options operator, arrow; PDF(A, alpha) end proc;
alpha -> PDF(A, alpha)
#Defining expectation fuction
E := proc (alpha) options operator, arrow; int(alpha*f(alpha), alpha = c .. d) end proc;
alpha -> int(alpha f(alpha), alpha = c .. d)
#g is a function of random variable α, where a and b are parameter


now I want to find the expectation of g and the first derivative of expectation of g,


diff(E(g), t)


I understand the way I have defined E(alpha) is improper. But please understand my intent and help! here is the maple file also

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