Consider a random variable X that has probability generating function
Px(z) = 87/256 + ( a + z/4)^4 + 88z^5 256
(a) Find the constant a. _____
(b) What is the probability mass function of X? ____
(c) Use the pgf Px (z) to compute E (X), E (X(X - 1)) and Var(X). _____
(d) Verify your calculation of Var(X) using the result of part (b).
