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May 22nd, 2018
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  1. f(x)=E[(X-x)^2]
  2. =E[X^2-2Xx+x^2]
  3. =E[X^2]-2xE[X]+x^2
  4. =E[X^2]-2xμ+x^2
  5. f(x) is minimum where f'(x)=0
  6. =>f'(x)=-2μ+2x=2(x-μ)=0
  7. =>x=μ
  8. =>f(x)=E[X^2]-μ^2=Var(X)
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