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Math Help - Expectation of cumulative function for N

  1. #1
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    Oct 2010
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    Expectation of cumulative function for N

    Hello!
    I have the following problem. Let X ~N(m,s^2) and define:

    Y = N(X)
    Z = e^{aX+b} N(X),

    where N is cumulative distribution function for standarized normal distribution (i.e. N(x)=\int_{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{-0.5 t^2} dt)
    What are the expectations of Y and Z (EY and EZ).

    (I know the answer but I am looking for advice/literature how to calculate this)
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  2. #2
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    Sep 2010
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    Hi,
    I used Fundementals of probability and stochastic processes by Dr. SAEED GHAHRAMANI. It was a good book, detailed with a lot of examples and you can find others too.
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