You roll a fair coin and a fair die simultaneously. Let X = 1 (X = 0) if the coin shows a head (tail) and Y equals the number showing on the die. Furthermore, let Z = 2X + Y . (a) Find the pmfs of X, Y , and Z. (b) Find E[X], E[Y ], and E[Z] using the pmfs of X, Y , and Z, respectively. Can you guess a general relationship between E[X], E[Y ], and E[Z]? (c) Find Var(X), Var(Y ), and Var(Z). Can you guess a general relationship between Var(X), Var(Y ), and Var(Z)? (d) Find E[1/Z] and Var(1/Z)