Suppose that Y1, Y2, . . . , Yn denote a

Chapter 10, Problem 129SE

(choose chapter or problem)

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

given by

\(f\left(y \mid \theta_{1}, \theta_{2}\right)=\left\{\begin{array}{l}

\left(\frac{1}{\theta_{1}}\right) e^{\left(i-\theta_{2}\right) \theta_{1}, y>\theta_{2}} \\

\end{array}\right.

Find the likelihood ratio test for testing $H_{0}: \theta_{1}=\theta_{1,0}$ versus $H_{a}: \theta_{1}>\theta_{1,0}$, with $\theta_{2}$ unknown.

Equation transcription:

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

$f(y|{\theta{}}_{1},{\theta{}}_{2})=\{{\ }_{0,}^{(\frac{1}{{\theta{}}_{1}}){e}^{(y-{\theta{}}_{2})/{\theta{}}_{1},}y>{\theta{}}_{2}}$

${H}_{0}:{\theta{}}_{1}={\theta{}}_{1,0}$

${H}_{a}:{\theta{}}_{1}>{\theta{}}_{1,0}$

${\theta{}}_{2}$

Text transcription:

Y{1}, Y{2}, ldots, Y{n}

f\y \heta{1}, theta{2})={\begin{array}{l}

(frac{1}{theta{1}}) e^(i-theta{2}) theta{1}, y>\theta{2}} \\

end{array}

H{0}: theta{1}=\theta{1,0}

H{a}: theta{1}>\theta{1,0}

theta{2}

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