The weekly demand for a magazine in a news shop can be represented by a random variable with the following probability function:

The owner of the shop buys each copy of the magazine for $4 and she sells it at a price of $6. If there is no possibility to return any unsold copies of the magazine, find the number of copies she should buy every week in order to maximize her expected profit.

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x+5 f(x)=1- x=7,8,9,10. 18