The random variable X can have the values 0 or 1, and the random variable Y can have the values 0, 1, or 2. The joint probability distribution of X and Y is given below: 0 1 2 0 0.1 A 0.15 1 B 0.1 C a) What are A, B, and C if E(X) = 0.45 and E(Y) = 1.00 ? To answer this question three equations with A, B, and C must be written. and == Show in the space below that these three equations are satisfied by A = 0.30, B = 0.2, and C = 0.15: b) Find the variance of 2X+3Y using the values for A, B, and C given in part (a); Var(2x+3)= c) How would the joint probabilities in the table have to be so that the random variables X and Y are independent and the marginal probabilities do not change? 0 1 2 0 1 2