Problem 13 Let $X_1, X_2, \dots, X_n$ be a sample from $G(1, \beta)$. a. Find the GLR test of $\beta = \beta_0$ against $\beta \neq \beta_0$. b. Find the GLR test of $\beta \leq \beta_0$ against $\beta > \beta_0$.
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Step 1: The likelihood function for the sample is given by: $$L(\beta) = \prod_{i=1}^n \frac{1}{\beta} e^{-x_i/\beta} = \frac{1}{\beta^n} e^{-\sum_{i=1}^n x_i/\beta}$$ Show more…
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