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.

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

a. Let X be 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 are demand and no unit is available in stock. Find the probability distributions of X and Y.

b. Find the expected value of X and the expected value of Y.

c. Assume that this appliance store makes a $60 profit on each air conditioner sold from the weekly available stock, but the store loses $20 for each unit sold on a special stockout order basis. Let Z be the profit that the store earns in the coming week from the sale of window air conditioners. Find the probability distribution of Z.

d. Find the expected value of Z.