A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold. The joint probability function of X and Y can be given by the following equation. P(X = 0, Y = 0) =1/6
P(X = 1, Y = 0) =1/12
P(X = 1, Y = 1) =1/6
P(X = 2, Y = 0) =1/12
P(X = 2, Y = 1) =1/3
P(X = 2, Y = 2) =1/6

Required:
Find the mean and variance of X.