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Math Help - pdf symmetric about a

  1. #1
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    pdf symmetric about a

    If X is a continuous random variable symmetric about some point a, how do I show that E(X) = a? Thanks.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Break the integral into two parts.

    E(X)=\int_{-\infty}^axf(x)dx+\int_a^{\infty}xf(x)dx

    Let x=a-u in the first integral and x=a+u in the second.

    Note that f(a-u)=f(a+u)
    Last edited by matheagle; February 20th 2010 at 08:47 PM.
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