Simple random sampling
Basic ideas.
Simplest random scheme where every subset of n units has the same chance of forming the sample, $p = \left( \binom{N}{n} \right)$ .Distribution of sample mean.
\[E(\bar{y}) = \mu\] \[Var(\bar{y}) = (1-f)\frac{\sigma^2}{n} \] \[E(s^2) = \sum^n_1 \frac{(y_i - \bar{y})^2}{n-1} \]With independent observations, the CLT ensures that $\bar{y}$ is approximately normal, which we can use to create CI(confidence interval)s etc.