Definition:Confidence Interval

Definition
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 $0 < \gamma < 1$.