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Math Help - find variance

  1. #1
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    find variance

    Fx(x)= 0 , x<1
    Fx(x)= (x^2-2x+2)/2 , 1<= x <2
    Fx(x)=1, x>=2

    calcualtae the variance of x.

    I drew the graph of this function. it is a mixed distribution with a point-mass at 1. But i dont know how to solve it.....
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  2. #2
    Moo
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    Hello,

    Find the pdf f of this function, by differentiating F_X

    Then the variance is :
    \int_0^2 x^2 f(x) ~dx-\left(\int_0^2 x f(x) ~dx\right)^2
    (definition of the variance)
    Last edited by Moo; May 1st 2009 at 03:22 AM. Reason: just a typo :p
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  3. #3
    MHF Contributor matheagle's Avatar
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    Almost (certainly, not).
    You're slipping, moo, you need the square.

    Quote Originally Posted by Moo View Post
    Hello,

    Find the pdf f of this function, by differentiating F_X

    Then the variance is :
    \int_0^2 x^2 f(x) ~dx-\left(\int_0^2 x f(x) ~dx\right)^{\color{red}2}

    This is the short cut formula for the variance.

    The definition is E\biggl(X-E(X)\biggr)^2
    Last edited by mr fantastic; April 30th 2009 at 10:07 PM. Reason: Put in the Red Square (a famous place in Moscow, by the way)
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