I have trouble understanding this notation, but here goes.
In estimating the true proportion or say the probability of an event, p.
Which I think is your ...
You sample n data points.
The proportion of successes from the data is
where Y is a binomial random variable with n number of trials and success probability our p.
is unbiased meaning that
and variance of is
SO plug in that value of Pi for my p and also the value for n.
Note that a standard deviations is the square root of the variance.