Consider rolling a 6-sided die with sides , , , , , and and define the random variable if s (0,0,0) if 8 ({1,2} if s {}. X (8) = 1 2 3 (a) Give the support of X. (b) Tabulate the probability distribution of X with a table of the form (e) Give the following probabilities: i. PX(X < 1/2) ii. PX(X 2.5) iii. Px(1 < X < 3) (f) Compute the expected value EX of X. (g) Compute the variance Var X of X. x Px (X