1. Suppose that you organise a game whereby a player rolls two dice and you pay the player the amount of the difference in the scores.

a. Determine the probability mass function of the positive difference between the scores obtained from rolling the two dice.

b. Calculate the mean value of X ,that is, the expected difference of the scores, in this case the expected or long run average payment per game.

c. What is the standard deviation of the scores , that is ,calculate the standard deviation of X.

d. Would you say that the distribution is symmetrical? Justify your answer.

e. Suppose that you change the players R2 toroll the two dice and then you pay them the difference in the scores .Let Y be the amount of money you make

(i)What are the possible values that Y can take?

(ii)What are your expected gain per game?