Suppose in a store with $n$ products we want to advertise one of the products to a customer. we know that for this customer the probability of buying the ith product is $p_{i}$. When the customer steps in the store we can advertise one of the product. If the jth product is advertised then the probability of buying it becomes $p_{j}$. The customer cant buy more than one of each product. We want to maximize the expected value of number of products that are bought. Which product should we advertise?
This the full problem. I still don't get what the final result should look like but for solving the problem I think we should define a $X_{i}$ showing that if the product is sold or not. If yes then the random variable is 1 and if no then it is 0. I think that it has something to do with conditional expectation but I don't know where to go from here