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Let X1,...,Xn be iid exp(θ) rvs. (a) Compute the pdf of Xmin. (b) Create an unbiased...

Let X1,...,Xn be iid exp(θ) rvs.

(a) Compute the pdf of Xmin.

(b) Create an unbiased estimator for θ based on Xmin. Compute the variance of the resulting estimator.

(c) Perform a Monte Carlo simulation of N= 10,0000 samples of your unbiased estimator from part (b) using θ = 2 and n = 100 to validate your answer. Include a histogram of the samples.

(d) Which is more efficient: your estimator from part (b) or the MLE for θ?

(e) Verify that the expected value of the exponential score function is 0 and compute the Fisher Information for θ. Is either estimator a MVUE for θ?

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