A store offers a new seasonal product featured. Let N be the random variable which means the number of clients who come to the store during the season, where N ~ Poi (19). It is estimated that the probability that a customer buys the new product is 0.38 regardless from a customer to another.
a) It is assumed here that the store has an unlimited supply of product . variables are random X and Y such that
X: The number of customers who purchase the product ;
Y: The number of customers who do not buy the product.
Are the variables X and Y independent ? Justify .
Answer: I think they are dependent, because there is a fixed number of costumers, and when the number of buyers changes, the number of non buyers changes too.
b) The store has a profit of 63millionforeachunitsold.Eachunsoldunitshouldbestoredfornextyearatacostof63millionforeachunitsold.Eachunsoldunitshouldbestoredfornextyearatacostof38 M .
Determine what the number of units stored should be to maximize its average profit.
Answer: Lets start with the pdf of Poisson distribution.
px(k)=exp(−α)α^k/k! , for k=0,1,...
α=19
px(k)=exp(−19)19^k/k! , for k=0,1,...
Now i don't know how to relate my 0.38 to the equation i just came up with...
Since 38% of the people buy, i need to first estimate how many costumers ill have with the Poisson distribution, then assume that 38% only will buy. So to maximize my profits, lets say there is 100 costumers estimated, ill only put 38, so ill sell everyone of them. But i don't know how to apply this logic to the problem
Your help is really appreciated!
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