Definition:Confidence Interval

Definition
Let $\theta$ be a population parameter.

Let $\mathbf X$ be a random sample from this population.

Let $I = \left({f \left({\mathbf X}\right) \,.\,.\, g \left({\mathbf X}\right)}\right)$ for some real-valued functions $f$, $g$.

$I$ is said to be a $100\gamma \%$ confidence interval for $\theta$ if:


 * $\displaystyle \mathbb P \left({f \left({\mathbf X}\right) < \theta < g \left({\mathbf X}\right)}\right) = \gamma$

where $0 < \gamma < 1$.