Question

Question (Neyman-Pearson lemma [5 marks]). Consider there is a singlevalued sample \( X \) from a distribution \[ f(\theta)=\frac{1}{\theta} e^{-x / \theta}, \] where \( \theta \) is unknown. Find a most powerful test for testing \[ \begin{array}{ll} H_{0}: & \theta=a ; \\ H_{1}: & \theta=b . \end{array} \] Without loss of generality, we assume that \( a<b \).

          Question (Neyman-Pearson lemma [5 marks]). Consider there is a singlevalued sample \( X \) from a distribution
\[
f(\theta)=\frac{1}{\theta} e^{-x / \theta},
\]
where \( \theta \) is unknown. Find a most powerful test for testing
\[
\begin{array}{ll}
H_{0}: & \theta=a ; \\
H_{1}: & \theta=b .
\end{array}
\]

Without loss of generality, we assume that \( a<b \).

Question (Neyman-Pearson lemma [5 marks]). Consider there is a singlevalued sample X from a distribution

f(θ)=(1)/(θ) e^-x / θ,

where θ is unknown. Find a most powerful test for testing

H0: θ=a ;

H1: θ=b .

Without loss of generality, we assume that a<b.

Added by Andrea H.

Introduction to Mathematical Statistics

Robert V. Hogg, Joseph W. McKean, Allen… 8th Edition

Chapter 8

Instant Answer

Solved by Expert David Nguyen

06/15/2022

Step 1

This is the exponential distribution with parameter \( \theta \). We are testing two hypotheses: - \( H_0: \theta = a \) - \( H_1: \theta = b \) where \( a < b \). Show more…

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Question (Neyman-Pearson lemma [5 marks]). Consider there is a singlevalued sample \( X \) from a distribution \[ f(\theta)=\frac{1}{\theta} e^{-x / \theta}, \] where \( \theta \) is unknown. Find a most powerful test for testing \[ \begin{array}{ll} H_{0}: & \theta=a ; \\ H_{1}: & \theta=b . \end{array} \] Without loss of generality, we assume that \( a<b \).