A store offers a new seasonal product as a feature. Let N be the random variable that denotes the number of customers who come to the store during the season, where N Poi(A). The probability that a customer will buy this new product is estimated to be B, independent of the customer. (Note: the values in red are given)

1. a) (3 points) It is assumed here that the store has an unlimited supply of this product. Let be the random variables X and Y such that X = the number of customers who buy the product; Y = the number of customers who do not buy the product. Are the variables X and Y independent? Justify.

1. b) (7 points) The store has a profit of C$ for each unit sold. Each unsold unit should be stocked for the next year at a cost of D$. Determine the value of the number of units stocked n that the store should have to maximize its average profit.