If one is given a non-uniform random variable with density $p(x)$ its expectation and error (when one tries to estimate this expectation are):
$$\mathbb{E}[f(x)] = \int_{\mathbb{R}}f(x)p(x) dx$$ and $$\epsilon_N (f) = \int_{\mathbb{R}}f(x)p(x)dx - \frac{1}{N}\sum_{n=1}^Nf(x_n)$$
The CLT gives the following results (I do not know how these are arrived at, I need help with precisely these two statements):
$$\epsilon \sim \frac{1}{\sqrt{N}}\phi\sigma_f$$ $$\sigma^2_f = \int_{\mathbb{R}}(f(x)-\bar{f})^2dx$$
$\phi$ may or may not be a standard normal here.