"Estimate of standard error of the proportion"
Please provide a proof/explanation of this formula. I'm particulary confused why $p ^\prime q ^\prime$ is in the numerator.
$$ \sigma_{p} = \sqrt \frac{p ^\prime q ^\prime}{n}$$
This is to the confidence interval for $p$.

Are you okay with standard formula definition of standard error ??

Yes.

And clarify this is for population or sample ?

Sample.
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Why does $V(X{i}) = E(X{i}^2)  E(X{i})^2$?

That is a standard way to compute the variance of a variable. The definition of variance is $V(X) := E( (XEX)^2 )$ And from this definition it is not difficult to prove the formula I used. It's easy to prove it from the
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