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Math Help - Integration with Probability.

  1. #1
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    Integration with Probability.

    Hello, I was wondering if anyone would be able to explain how the solution got from the E(Profit) = integral line to the next line.
    A full step by step of the entire question would be preferred.
    Thank you so much for your time.
    -GaleonTiger


    Integration with Probability.-question.jpg
    Last edited by mr fantastic; March 8th 2011 at 04:40 AM. Reason: Begging for help in title.
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  2. #2
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    Lump the integral terms together using \int_{-\infty}^x g+\int^{\infty}_x g =\int_{-\infty}^\infty g.

    Then use the fact that \mathbb{P}(X \geq x)=\int_{x}^\infty f_X(u) du where f_X is the pdf of X.
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