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...

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In a game of repeated die rolls, a player is allowed to roll astandard die up to n times, where n is determined prior to thestart of the game. On any roll except the last, the player maychoose to either keep that roll as their final score, or continuerolling in hopes of a higher roll later on. If the player rolls all ntimes, then after the nth roll, the player must keep that roll astheir final score. A player always acts to maximize theirexpected final score. Finally, let V denote the final score in agame with a max of n rolls allowed.a) Compute E[V2] with justification.