3. A customer entering an electronics store will buy a flat screen TV with probability 0.3. Sixty percent of the customers buying a flat screen TV will spend $750.00 and 40% will spend $400.00. Let X denote the amount spent on flat screen TVs by two random customers entering the store.

(a) Find the PMF of X. (Hint. SX = {0, 400, 750, 800, 1150, 1500} and P(X = 400) = 2 × 0.7 × 0.3 × 0.4.)

(b) Find the mean value and variance of X.