Solution Found!
Let Y1, Y2, . . . , Yn denote a random sample
Chapter 9, Problem 82E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from the density function given by
\(f(y \mid \theta)=\left\{\begin{array}{ll} \left(\frac{1}{\theta}\right) r y^{r-1} e^{-y^{r} / \theta}, & \theta>0, y>0 \\ 0, & \text { elsewhere } \end{array}\right.\)
where is a known positive constant.
a Find a sufficient statistic for \(\theta\).
b Find the MLE of \(\theta\).
c Is the estimator in part (b) an MVUE for \(\theta\) ?
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
f(y \mid \theta)={1\theta\right) r y^r-1 e^-y^r / \theta, & \theta>0, y>0 0, elsewhere
\theta
\theta
\theta
Questions & Answers
QUESTION:
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from the density function given by
\(f(y \mid \theta)=\left\{\begin{array}{ll} \left(\frac{1}{\theta}\right) r y^{r-1} e^{-y^{r} / \theta}, & \theta>0, y>0 \\ 0, & \text { elsewhere } \end{array}\right.\)
where is a known positive constant.
a Find a sufficient statistic for \(\theta\).
b Find the MLE of \(\theta\).
c Is the estimator in part (b) an MVUE for \(\theta\) ?
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
f(y \mid \theta)={1\theta\right) r y^r-1 e^-y^r / \theta, & \theta>0, y>0 0, elsewhere
\theta
\theta
\theta
ANSWER:
Step 1 of 4
a.
Define the joint pdf of 
