In the casino game chuck-a-luck, three fair six-sided dice are rolled. One possible bet is $1 on fives, and the payoff is equal to $1 for each five on that roll. In addition, the dollar bet is returned if at least one five is rolled.
The dollar that was bet is lost only if no fives are rolled. Let X denote the payoff for this game. Then X can equal −l, l, 2, or 3.
(a) Determine the pmf f(x).
(b) Calculate μ, σ2, and σ.
(c) Depict the pmf as a probability histogram.