Consider a game in which a red die and a blue die are rolled. Letx_Rdenote the value showing on the uppermost face of the red die, and definex_Bsimilarly for the blue die.

(a) The probability distribution ofx_Ris as follows.x_Rp(x_R)11/621/631/641/651/661/6Find the mean, variance, and standard deviation ofx_R. (Round your answers to three decimal places.)

Mean =

Variance =

Standard deviation =

(b) What are the values of the mean, variance, and standard deviation ofx_B? You should be able to answer this question without doing any additional calculations. (Round your answers to three decimal places.)

Mean =

Variance =

Standard deviation =

(c) Suppose that you are offered a choice of the following two games.Game 1:Costs $7 to play, and you winy₁dollars, wherey₁=x_R+x_B.Game 2:Doesn't cost anything to play initially, but you "win"4y₂dollars, wherey₂=x_R-x_B. Ify₂is negative, you must pay that amount; if it is positive, you receive that amount.

For Game 1, the net amount won in a game isw₁=y₁- 7 =x_R+x_B- 7. What are the mean and standard deviation ofw₁? (Round your answers to three decimal places.)

Mean =

Standard deviation =

(d) For Game 2, the net amount won in a game isw₂=4y₂=4(x_R-x_B). What are the mean and standard deviation ofw₂? (Round your answers to three decimal places.)

Mean =

Standard deviation =

(e) Based on your answers to Parts (c) and (d), which game would you choose if you are quite a risky person?

Game 1

Game 2