When a tetrahedral die is thrown, the number on the face on which it lands, X, has probability distribution as shown, with E(X)=2.5 and Var(X) = 1.25. 1 P(X-x) 0.25 2 3 4 0.25 0.25 0.25

(a) Find the probability distribution of S, the sum of the two numbers obtained when the die is thrown twice, where S-X,+X, and illustrate it by drawing a vertical line graph. Find E(S) and Var(S).

(b) Find the probability distribution of D, where D is double the number on which the die lands when it is thrown once. Illustrate by drawing a vertical line graph. Find E(D) and Var(D).