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Math Help - Expected Profit

  1. #1
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    Expected Profit

    Sorry, I already asked a question today, but it would be awesome if someone could help me with this one, I feel like I'm close:

    The annual profit Y(in $100,000) can be expressed as a continuous function of drug demand x(in 1,000): Y(x) = 2(1-e^(-2x)). Suppose the demand for their drug has the probability function: f(x)= 6e^(-6x), x>0. Find the company's expected annual profit.

    So do I have to start by doing ? I'm sure I have the upper bound wrong...
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  2. #2
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    The way I see this problem, it is a mixed distribution where the given profit function Y is conditional on X:

    f_{Y|X}(y|x)=2(1-e^{-2x})

    and therefore to find E(Y) you need first to find marginal distribution f_Y(y) and then go from there.

    But I may be totally wrong!
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  3. #3
    Moo
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    Hello,

    E[Y]=E[E[Y|X]]=E[E[2(1-e^{-2X})|X]]=E[2(1-e^{-2X})], which is the formula alakaboom1 wrote.
    As for the boundaries, it should rather be on the whole set of real numbers.
    Then since f(x)=0 if x<0, the boundaries will indeed go from 0 to infinity.

    Volga : there's something disturbing in what you wrote. 2(1-e^{-2x}) is not a pdf. We just have that Y=2(1-e^{-2X}), so in order to find Y's pdf, there's a change of variable to make in X's pdf
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  4. #4
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    Sorry!
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