subsets probability question 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 $p$.

I think the answer is:
a) $E[\bar{p}] = p$,
b) Var$[\bar{p}] = \frac{\sqrt{p(1-p)}}{\sqrt{n}}$.
I believe the answer can be found on page 10 of
http://math.arizona.edu/~faris/stat.pdf
~JD
