A fair 5-sided (1, 2, 3, 4, 5) die is rolled and, independently, a fair coin is tossed. Let V be the value of the die if the coin is H and 3 minus the value of the die if the coin is T.

(a) (2 pts) Calculate the conditional PMFs pVH(v) and pVT(v).

(b) (1 pt) Use the total probability theorem and part (a) to get pV(v).

(c) (2 pts) Calculate the conditional expectations E [VH] and E [VT].

(d) (1 pt) Use total expectation and part (c) to get E [V].

(e) (3 pts) Calculate var (V) by first calculating E [V 2 ] using total expectation