Consider a set $\Omega$ with $N$ distinct members, and a function $f$ defined on $\Omega$ that takes the values 0,1 such that $ \frac{1}{N} \sum\_{x \in \Omega } f(x)=p$. For a subset $S⊆Ω$ of size n, define the sample proportion
$p:= p(S)= \frac{1}{n} \sum\_{x\in S} f(x)$.
If each subset of size $n$ is chosen with equal probability, calculate the expectation and standard deviation of the random variable $p$.