1. Consider the following game: two fair six sided dice are rolled. If you roll "snake eyes" you win 14 dollars, if you roll any other double you win 2 dollars, and if you do not roll a double you lose one dollar.

(a)let x be the discrete random variable representing the amount of money won in a given roll. define probability distribution of x, p(x).

(b)What is the mean, or expected value of x? Interpret your results in terms of how you will fair playing the game in the long run.

(c)What is the standard deviation of x?

(d)Now consider changing the amount of money won in the event of rolling snake eyes. What amount of money would ensure that in the long-run you break even?