Consider a single roll of a pair of 6-sided dice and a flip of two fair coins. Let Xi be the outcome for die i,i = 1,2, and let Ci be the number of heads obtained by flipping coin i,i = 1,2. Define the following

S1 = X1 + 4C1

S2 = X2 + 4C2

T = S1 + S2 = X1 + X2 + 4C1 + 4C2

Compute E[T], Var[T], and P(T 16).