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Let X1,...,Xn be iid exp(θ) rvs. (a) Compute the pdf of Xmin. I have the pdf...

Let X1,...,Xn be iid exp(θ) rvs.

(a) Compute the pdf of Xmin.

I have the pdf

(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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