Statistics Graduate Level Quiz
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STATISTICAL INFERENCE
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Independent observations have exponential density f(x;θ)=θe−θxf(x;\theta)=\theta e^{-\theta x} for x>0x>0, where θ>0\theta>0 is the rate. The model is reparameterized by the mean η=1/θ\eta=1/\theta. What are the Fisher information for η\eta in a sample of size nn and the corresponding Cramér–Rao bound for unbiased estimation of η\eta?
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