Question

15. The plastic arrow on a spinner stops rotating to point at a number in a game of chance. Let X denote the pay off. The probability distribution of the pay off is as follows: 23 X: | 1 | 2 | 3 Probability: | .25.50 .25 ((c) 2.00 (d) 2.50 (e) 3.00 The expected payoff, E(X), is: (a) 1.00 (b) 1.50 16. (continuation) The variance of X, Var(X), is: (a) .50 )(b) 1.00 (c) 1.50 (d) 2.00 (C) 2.50

Answer 1

Expected payoff : E(X)= xP(x) = (1 * 0.25) + (2 * 0.5) + (3 * 0.25) = 2 Var(x) = E(X²) - (E(X))2 Now, E(X) = x?P(x) = (1+0.25) + (4 * 0.5) + (9* 0.25) = 4.5 So, Var(X) = 4.5 – (22) = 4.5 – 4= 0.5