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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Originally Posted by Duke 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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