Consider a game in which a red die and a blue die are

Chapter 0, Problem 7.45

(choose chapter or problem)

Consider a game in which a red die and a blue die are rolled. Let xR denote the value showing on the uppermost face of the red die, and define xB similarly for the blue die. a. The probability distribution of xR is xR 1/1 1/2 1/3 1/4 1/5 1/6 p(xR) 1/6 1/6 1/6 1/6 1/6 1/6 Find the mean, variance, and standard deviation of xR. b. What are the values of the mean, variance, and standard deviation of xB? (You should be able to answer this question without doing any additional calculations.)c. Suppose that you are offered a choice of the followingtwo games:Game 1: Costs $7 to play, and you win y1 dollars, wherey1 xR xB.Game 2: Doesnt cost anything to play initially, but youwin 3y2 dollars, where y2 xR xB. If y2 isnegative, you must pay that amount; if it is positive,you receive that amount.For Game 1, the net amount won in a game is w1 y1 7 xR xB 7. What are the mean and standarddeviation of w1?d. For Game 2, the net amount won in a game is w2 3y2 3(xR xB). What are the mean and standard deviationof w2?e. Based on your answers to Parts (c) and (d), if you hadto play, which game would you choose and why?