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Math Help - Conditional Expectation

  1. #1
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    Conditional Expectation

    I am trying to figure out the following problem but I don't understand exactly how to deal with the conditional expectation. If X is a random variable with CDF F(x) then what is E[ X | X > w]?
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  2. #2
    MHF Contributor matheagle's Avatar
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    I believe it's just

     {E(XI(X>w))\over P(X>w)}= {\int_w^{\infty}xf(x)dx\over 1-F(w)}

    where the I is an indicator function, which is one when X exceeds w.
    So you're just integrating X over the region w to infinity.
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