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alright here is the source I found . http://isites.harvard.edu/fs/docs/icb.topic515975.files/Proof that Sample Variance is Unbiased.pdf
At the last third / forth paragraph , it says expected value of the square of something is not equal to the square of the expected value . Which is true . However what if it is expected value of a mean . or expected value of an expected value ?
Is that alright to says that E(mean^2) = Mean^2 = E(X)^2 And finally E(X^2)-E(X)^2 = Var(X) = population variance ?
And I got how Var ( summation x ) = summation Var x as shown , any idea?
At the last third / forth paragraph , it says expected value of the square of something is not equal to the square of the expected value . Which is true . However what if it is expected value of a mean . or expected value of an expected value ?
Is that alright to says that E(mean^2) = Mean^2 = E(X)^2 And finally E(X^2)-E(X)^2 = Var(X) = population variance ?
And I got how Var ( summation x ) = summation Var x as shown , any idea?