# Sampling design

In the theory of finite population sampling, a sampling design specifies for every possible sample its probability of being drawn.

## Mathematical formulation

Mathematically, a sampling design is denoted by the function $P(S)$ which gives the probability of drawing a sample $S.$

## An example of a sampling design

During Bernoulli sampling, $P(S)$ is given by

$P(S) = q^{N_\text{sample}(S)} \times (1-q)^{(N_\text{pop} - N_\text{sample}(S))}$

where for each element $q$ is the probability of being included in the sample and $N_\text{sample}(S)$ is the total number of elements in the sample $S$ and $N_\text{pop}$ is the total number of elements in the population (before sampling commenced).