In a game of repeated die rolls, a player is allowed to roll a standard die up to n times, where n is determined prior to the start of the game. On any roll except the last, the player may choose to either keep that roll as their final score, or continue rolling in hopes of a higher roll later on. If the player rolls all n times, then after the nth roll, the player must keep that roll as their final score. A player always acts to maximize their expected final score. Finally, let V, denote the final score in a game with a max of n rolls allowed.
a. Compute E[V2] with justification.
b. Compute E[V3] with justification.
c. Find the smallest n such that E[V] >= 5
d. Find the smallest n such that E[V]n.