Let Y1, Y2, . . . , Yn denote a random sample

Chapter 9, Problem 88E

(choose chapter or problem)

Let $Y_{1}, Y_{2}, \ldots, Y_{n}$ denote a random sample from the probability density function

$f(y \mid \theta)=\left\{\begin{array}{ll} (\theta+1) y^{9}, & 0<y<1, \theta>-1 \\ 0, & \text { elsewhere } \end{array}\right.$

Find the MLE for $\theta$. Compare your answer to the method-of-moments estimator found in Exercise $9.69.$

Equation Transcription:

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

$f(y|\theta{})=$ { ${\ }_{0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ elsewhere}^{(\theta{}+1){y}^{9},\ \ \ 0\ <\ y\ <1,\ \theta{}\ >\ -\ 1\ \ \ \ \ \ \ }$

$\theta{}$

Text Transcription:

Y1, Y2,...,Yn

\(f(y \mid \theta)=(\theta+1) y^9, & 0<y<1, \theta>-1 0, elsewhere

\theta

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