Consider the random variables x_R and x_B defined in the previous exercise.

a. Suppose that you are offered a choice of the following two games:

Game 1: Pay $7 to play, and you win y1 dollars, where y₁ = x_R + x_B.

Game 2: Doesn’t cost anything to play initially, but you “win” 3y₂ dollars, where y₂ = x_R + x_B. If y₂ 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 w₁ = y₁ - 7 = x_R + x_B - 7. What are the mean and standard deviation of w₁?

b. For Game 2, the net amount won in a game is w₂ = 3y₂ = 3(x_R - x_B). What are the mean and standard deviation of w₂?

c. Based on your answers to Parts (a) and (b), if you had to play, which game would you choose?

Explain your reasoning.