Let V(X, ) be any pivotal quantity [i.e., have a fixed probability distribution independent of (, )],

Let V(X, θ) be any pivotal quantity [i.e., have a fixed probability distribution independent of (θ, ϑ)], and let B be any set in the range space of V with probability P(V ∈ B) = 1 − α. Then the sets S(x) defined by

θ ∈ S(x) if and only if V(θ, x) ∈ B (6.75)

are confidence sets for θ with confidence coefficient 1 − α.