suppose you play a game G in which you roll 100 dice, and the payoff is the number of dice that come up " 6 ." What is the variance of this game?

Answer 1

The probability of a 6 on a single roll is 1/6. Thus, the variance on a single roll is p(1-p), and the variance on 100 rolls is 100 p(1-p) = 100 1/6 5/6 = 500/36 = 125/9 = 13 8/9