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A store offers a new seasonal featured product. Let N be the random variable which designates...

A store offers a new seasonal featured product. Let N be the random variable which designates the number of customers who come to the store during the season, where N ∼ Poi (30). It is estimated that the probability that a customer will buy this new product is 0,7 and this independently of one customer to another.

a) It is assumed here that the store has an unlimited stock of this product. Let X and Y be the random variables 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? To justify.

b) The store has a profit of 25 $ for each unit sold. Each unsold unit should be stored for next year at the cost of 15$. Determine the value of the number of units stored n that the store should have to maximize its average profit.

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