Question

Suppose that $X_1, \dots, X_n$ are iid having the common exponential pdf $f(x; \theta) = \theta^{-1} \exp\{-x/\theta\}I(x > 0)$ where $\theta(> 0)$ is assumed unknown. With preassigned $\alpha \in (0, 1)$, derive a level $\alpha$ LR test for a null hypothesis $H_0: \theta = \theta_0(> 0)$ against an alternative hypothesis $H_1: \theta \neq \theta_0$ in the implementable form. LR: likelihood ratio UMP: Uniformly Most Powerful

          Suppose that $X_1, \dots, X_n$ are iid having the common exponential pdf
$f(x; \theta) = \theta^{-1} \exp\{-x/\theta\}I(x > 0)$ where $\theta(> 0)$ is assumed unknown. With
preassigned $\alpha \in (0, 1)$, derive a level $\alpha$ LR test for a null hypothesis $H_0: \theta = \theta_0(> 0)$ against an alternative hypothesis $H_1: \theta \neq \theta_0$ in the implementable form.
LR: likelihood ratio
UMP: Uniformly Most Powerful

$Suppose that X1, …, Xn are iid having the common exponential pdf f(x; θ) = θ^-1{-x/θ}I(x > 0) where θ(> 0) is assumed unknown. With preassigned α∈ (0, 1), derive a level α LR test for a null hypothesis H0: θ = θ0(> 0) against an alternative hypothesis H1: θ≠θ0 in the implementable form. LR: likelihood ratio UMP: Uniformly Most Powerful$

Added by Kristy L.

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