# Data Collection

1. outcome of an experiment: sample space ${\displaystyle s\in {S}}$
2. experiment ${\displaystyle \equiv }$ sampling
1. define population: ${\displaystyle \pi \in \Pi }$
2. define measurement on units of the population: ${\displaystyle x(\pi )}$
3. randomly draw n units: ${\displaystyle \pi _{1},\pi _{2},...,\pi _{n}{\rightarrow }x(\pi _{1}),x(\pi _{2}),...,x(\pi _{n}){\rightarrow }x_{1},x_{2},...x_{n}}$
3. probability model for the outcomes of the experiment
1. experiment${\displaystyle \{P_{\theta }:\theta \in \Omega \}}$ (statistical model)
2. sampling ${\displaystyle \{f_{\theta }:\theta \in |Omega\}}$