Theoretical results for the mean and standard deviation of a sample proportion

Let’s assume we have a random variable X that comes from a binomial process with sample size n and probability of success .

We are assuming we already know that E(X) = and SD(X) =

Some key variable algebra rules:

where c is an arbitrary constant

and so

So by definition of sample proportion

We can take out the constant and apply what we know about the binomial random variable:

Similarly

SD() =