An ordinary fair die is rolled. If the die shows an odd number then S, the score awarded, is equal to that number. If the die shows an even number, then the die is rolled again. If on the second roll it shows an odd number, then that is the score awarded. If the die shows an even number on the second roll, the score awarded is equal to half of that even number.

a. List the possible values of S and draw up a probability distribution table.

b. Find P[S > E(S)].

c. Calculate the exact value of Var(S).