Question: If L(x) and U(x) satisfy P(L(X) ) = 1 - 1 and P(U(X) ) = 1 - 2, and L(x) U(x) for

If L(x) and U(x) satisfy Pθ(L(X) ≤ θ) = 1 - α1 and Pθ(U(X) ≥ θ) = 1 - α2, and L(x) ≤ U(x) for all z, show that Pθ(L(X) ≤ θ ≤ U(X)) = 1 - α1 - α2.

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