Answer: Let Y1, Y2, . . . , Yn be a random sample from a
Chapter 9, Problem 63E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) be a random sample from a population with density function
\(f(y \mid \theta)=\left\{\begin{array}{ll}\frac{3 y^{2}}{\theta^{3}}, & 0 \leq y \leq \theta \\0, & \text { elsewhere }\end{array}\right.\)
In Exercise 9.52 you showed that \(Y_{(n)}=\max \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)\) is sufficient for \(\theta\).
a Show that \(Y_{(n)}\) has probability density function
\(f_{(n)}(y \mid \theta)=\left\{\begin{array}{cc}\frac{3 n y^{3 n-1}}{\theta^{3 n}}, & 0 \leq y \leq \theta, \\0, & \text { elsewhere }\end{array}\right.\)
b Find the MVUE of \(\theta\).
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