Suppose we roll two four-sided dice, that is, each die has 4 sides, numbered 1,2,3,4. Let X1 and X2 be the numbers that appear on the first and second die respectively. Let Z = max(X1, X2), that is Z is the larger of the two numbers rolled.

(a) Find the probability mass function, fZ(z), for Z.

(b) FindFZ(z)=P(Zz)for

(c) Draw a sketch plot of FZ(z).

(d) Find E[Z].

(e) Find Var(Z).