Let f be the probability function of a discrete random variable X with range

{m,m + 1,m + 2,…, n}, and let g be a function defined on the same set. Write a program to calculate the expectation E[g(X)]. As an application,

(i) solve Example 4.17;

(ii) carry out the calculations necessary in Exercise 18 of Section 4.4;

(iii) calculate the expectations E(3X + 7), E(5X3 − 2), E(Y3), E(

√

Y), and E(eY ) for the random variables X and Y defined in Exercise 20 of Section 4.4.