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.