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Math Help - Expected value of squared normal

  1. #1
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    Expected value of squared normal

    I need to find the expected value a N~(0,1) squared distribution. I realize this is a Chi Square distribution with k = 1. The expected value is therefore k = 1. However, I am having trouble taking the following integral to find the expected value:

    Integrate y*exp(-y^4) from -inf to inf.

    I'm sure there is a trick somewhere to figure it out but i can't find it!

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mrfloyd View Post
    I need to find the expected value a N~(0,1) squared distribution. I realize this is a Chi Square distribution with k = 1. The expected value is therefore k = 1. However, I am having trouble taking the following integral to find the expected value:

    Integrate y*exp(-y^4) from -inf to inf.

    I'm sure there is a trick somewhere to figure it out but i can't find it!

    Thanks
    The expected value of x^2 is:

    E(x^2)=\int_{-\infty}^{\infty} x^2 p(x) \; dx

    which in this case comes to the variance of x

    CB
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  3. #3
    MHF Contributor matheagle's Avatar
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    The integral of an odd function from minus infinity to infinity is zero.
    But I'm not sure if that is what you're asking.
    Last edited by matheagle; January 25th 2010 at 03:29 PM.
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