Consider a game in which a red die and a blue die are rolled. Let X_R denote the

Question

Consider a game in which a red die and a blue die are rolled. Let X_R denote the value showing on the uppermost face of the red die, and define X_B similarly for the blue die (a) The probability distribution of x_R is as follows. Find the mean, variance, and standard deviation of x_R. (Round your answers to three decimal places.) Mean = 3.5 Variance = 2.917 Standard deviation = 1.709 (b) What are the values of the mean, variance, and standard deviation of x_B? You should be able to answer this question without doing any additional calculations. (Round your answers to three decimal places.) Mean = 3.5 Variance = 2.917 Standard deviation = 1.709 (c) Suppose that you are offered a choice of the following two games. Game 1: Costs $7 to play, and you win y_1 dollars, where y_1 = x_R + x_B. Game 2: Doesn't cost anything to play initially, but you "win" 2y_2 dollars, where y_2 = x_R - x_B. If y_2 is negative, you must pay that amount; if it is positive, you receive that amount. For Game 1, the net amount won in a game is w_1 = y_1 - 7 = x_R + x_B - 7. What are the mean and standard deviation of w_1? (Round your answers to three decimal places.) Mean = Standard deviation = (d) For Game 2, the net amount won in a game is w_2 = 2y_2 = 2(x_R - x_B). What are the mean and standard deviation of w_2? (Round your answers to three decimal places.) Mean = Standard deviation =

Explanation / Answer

c) for mean of Xa+xb-7=3.5+3.5-7=0

std deviation=(1.7092+1.7092)1/2 =2.415

d) mean =2(xa-xb) =2(3.5-3.5)=0

std deviation =(4*1.7092+4*1.7092)1/2 =4.830

as std deviation in part d is higher it i s more risky

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