Based on past sales experience, an appliance store stocks five window air conditioner units for the coming week. No orders for additional air conditioners will be made until next week. The weekly consumer demand for this type of appliance has the probability distribution given in the file P04_56.xlsx. a. Let Xbe the number of window air conditioner units left at the end of the week (if any), and let Y be the number of special stockout orders required (if any), assuming that a special stockout order is required each time there is a demand and no unit is available in stock. Find the probability distributions of Xand Y. b. Find the expected value of X and the expected value of Y.

Weekly air conditioner demand Number demanded 0 1 2 3 4 5 6 7 8 >=9 Probability 0.05 0.05 0.08 0.16 0.30 0.16 0.10 0.05 0.05 0.00