Let Y1, Y2, . . . , Yn denote a random sample
Chapter 9, Problem 50E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from the uniform distribution over the interval \(\left(\theta_{1}, \theta_{2}\right)\). Show that \(Y_{(1)}=\min \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)\) and \(Y_{(n)}=\max \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)\) are jointly sufficient for \(\theta_{1}\) and \(\theta_{2}\).
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