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Math Help - Show this is a valid pdf

  1. #1
    Junior Member
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    Show this is a valid pdf

    Show that

    fY(y) = 1/(y^2), y >= 1

    is a valid pdf but that Y does not have a finite expected value.
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  2. #2
    Super Member Anonymous1's Avatar
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    We know that valid pdfs integrate to 1.

    \int_1^{\infty} \frac{1}{y^2}dy = \frac{-1}{y}|_{1}^{\infty} = 1

    E[Y]= \int_1^{\infty} y\times \frac{1}{y^2}dy =  \int_1^{\infty} \frac{1}{y}dy= \ln(y)|_{1}^{\infty} = \infty

    Let me know if you have questions.
    Anonymous
    Last edited by Anonymous1; March 16th 2010 at 03:43 PM.
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