5. (18 pts) In a three-spot Keno game offered locally\', the net winnings, X, in

Question

5. (18 pts) In a three-spot Keno game offered locally', the net winnings, X, in each SI bet has the following probability mass function P(X = x) 57 S45 4,108 570 4,108 3,481 4,108 $1 -$1 a. Write an expression for the mean net winnings in a $1 three-spot bet. Evaluate such (give a decimal). b. Write an expression for the variance of net winnings in a S1 three-spot bet. Evaluate such (give a decimal). In video Keno games in Rapid City and Deadwood, at least at one time (I haven't verified recently). 6

Explanation / Answer

a) E(X) = 45 * (57/4108) + 1 * (570/4108) - 1 * (3481/4108) = -0.084

b) E(X2) = 452 * (57/4108) + 12 * (570/4108) + (-1)2 * (3481/4108) = 29.0837

Var(X) = E(X2) - (E(X))2 = 29.0837 - (-0.084)2 = 29.077

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