1. Jessica Williams, manager of Kitchen Appliances for the Midtown Department Store, feels that her inventory levels of stoves have been running higher than necessary. Before revisiting the inventory policy for stoves, she records the number sold each day over a period of 25 days in a excel file (here Download here). (1 point)

a. If we define a random variable X as the number of units sold per day, use these data to estimate the probability distribution (hint: use pivot table will be the easiest for this) and cumulative distribution for X in a tabular format, and calculate the Expectation of X.

b. Currently, Jessica is keeping 50 units in stock, and she will place another order of 45 units once the inventory level drops to 5 units. How frequent does Jessica place an order each month (25 work days)? (Hint: use the notion of expectation.)

c. The profit for each stove sold is $150. For each unit sold, there is a 5% chance that the unit will be returned by the customer for full refund. The returned unit will then be sold to a discount store at a lower profit of $50. What is the expected daily profit from stove sales? (Hint: define another variable Y as the actual profit for each unit sold taking into account the returns.)

Day Number of stoves sold 1 5 2 2 3 2 4 3 5 3 6 6 7 4 8 4 9 3 10 5 11 5 12 4 13 4 14 4 15 4 16 2 17 4 18 3 19 5 20 2 21 3 22 3 23 3 24 4 25 5