= Solution
A $100\gamma\%$ <confidence interval> is a pair of statistics $L(X)\le U(X)$ whose random interval satisfies
$$
\boxed{\mathbb P_\theta\{L(X)\le\theta\le U(X)\}\ge\gamma\quad\text{for every allowed }\theta.}
$$
An exact confidence interval has equality throughout. The probability refers to repeated sampling at a fixed unknown parameter; the endpoints are random before observation. It is not a posterior probability assigned to the parameter after seeing the data. Here $0<\gamma<1$.
Back to article page
