Solved: Let Y1, Y2, . . . , Yn denote independent and
Chapter 9, Problem 54E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote independent and identically distributed random variables from a power family distribution with parameters \(\alpha\) and \(\theta\). Then, as in Exercise 9.43, if \(\alpha,\ \theta\ >\ 0,\)
\(f(y \mid \alpha, \theta)=\left\{\begin{array}{ll}\alpha y^{\alpha-1} / \theta^{a}, & 0 \leq y \leq \theta \\0, & \text { elsewhere }\end{array}\right.\)
Show that max \((Y_{1}, Y_{2}, \ldots, Y_{n})\) and \(\prod_{i=1}^{n} Y_{i}\) are jointly sufficient for \(\alpha\) and \(\theta\).
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