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Math Help - proving equation

  1. #1
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    proving equation

    let Y1,.....,Yn be random variables and let Y be the sample mean

    show that sum(Yi-Y)^2 = sum(Yi^2)-nY^2 (the sum from 1 to n)

    LHS=Sum(Yi^2+Y^2-2Yi*Y)=Sum(Yi^2)+Sum(Y^2)-2Sum(Yi*Y)

    Help to complete
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: proving equation

    Quote Originally Posted by Duke View Post
    let Y1,.....,Yn be random variables and let Y be the sample mean

    show that sum(Yi-Y)^2 = sum(Yi^2)-nY^2 (the sum from 1 to n)

    LHS=Sum(Yi^2+Y^2-2Yi*Y)=Sum(Yi^2)+Sum(Y^2)-2Sum(Yi*Y)

    Help to complete
    Sum(Y^2)=nY^2

    2Sum(Yi*Y)=2Y*Sum(Yi)=2Y*nY=2nY^2

    So, Sum(Yi-Y)^2=Sum(Yi^2)+nY^2-2nY^2=Sum(Yi^2)-nY^2
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  3. #3
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    Re: proving equation

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