Statistics / Mathematical Statistics with Applications 7 / Chapter 9 / Problem 52E

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Let Y1, Y2, . . . , Yn be a random sample from a

Chapter 9, Problem 52E

(choose chapter or problem)

Let $Y_{1}, Y_{2}, \ldots, Y_{n}$ be a random sample from a population with density function

$f(y \mid \theta)=\left\{\begin{array}{ll}\frac{3 y^{2}}{\theta^{3}}, & 0 \leq y \leq \theta \\0, & \text { elsewhere }\end{array}\right.$

Show that $Y_{(n)}=\max \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)$ is sufficient for $\theta$.

Equation Transcription:

${Y}_{1},\ {Y}_{2},\ ....,\ {Y}_{n}$

$f\ (y\ |\ \theta{})=$ { ${\ }_{0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ elsewhere.}^{\frac{3{{y}^{2}}^{\ }}{{\theta{}}^{3}},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\ \leq{}\ y\ \leq{}\ \theta{},}$

${Y}_{(n)}$ = max $\left({{Y}_{1},\ {Y}_{2},\ ....,\ {Y}_{n}}\right)$

$\theta{}$

Text Transcription:

Y_1, Y_2, …., Y_n

f(y mid | theta) = {frac{3 y^{2}}{8^{3}}, & 0 leq y leq theta 0 & text { elsewhere}

Y_(n) = max (Y_1, Y_2, …., Y_n)

theta

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