Consider a discrete uniform random variable X with a minimum value of 3 and maximum value of 8. In symbols, let X U{3, 8}.

a) Determine the probability: P(X = 5).

b) Determine the expected value (mean) of X.

c) Determine the probability: P(4 <= X <= 6).

d) Let X U{3, 8} and Y U{3, 8}, and define a new random variable Z = X + Y (i.e. the outcome of Z is the sum of the outcomes from X and Y. Would Z follow a discrete uniform distribution? If so, state the parameters for this distribution. If not, justify your answer. (Hint: it may help to think about the sum of two six-sided dice instead.)