You are playing a game that uses a fair 12-sided die whose faces are numbered 1, 2, . … 12 The value of a roll is the number showing on the top of the die when it comes to rest. Give all answers as simplified fractions. (a) Let X be the value of one roll of the die. Compute E[X] and Var(X) (b) Let Y be the sum of the values of 4 independent rolls of the die. Compute E[Y ] and Var(Y ). Use independence, and state precisely where in your computation you are using it. (c) Let Z be the average of the values of 4 independent rolls of the die. Compute EIZ] and Var(Z). Use independence, and state precisely where in your computation you are using it.