\begin{definition}[Definition:Confidence Interval]
Let $\theta$ be a population parameter of some population.
Let $\mathbf X$ be a random sample from this population.
Let $I = \openint {\map f {\mathbf X} } {\map g {\mathbf X} }$ for some real-valued functions $f$, $g$.
$I$ is said to be a '''$100\gamma \%$ confidence interval''' for $\theta$ if: 
:$\map \Pr {\theta \in I} = \gamma$
where $0 < \gamma < 1$.
\end{definition}