Survival times have the exponential distribution with pdf (x; ) = e x for x 0,
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Survival times have the exponential distribution with pdf ƒ(x; λ) = λe –λx for x ≥ 0, where λ > 0 is unknown. However, we wish to estimate the mean μ = 1/λ based on the random sample X1, X2, …, Xn, so let’s re-express the pdf in the form (1/μ)e–x/μ.
a. Find the information in a single observation and the Cramér–Rao lower bound.
b. Determine the mle of μ.
c. Find the mean and variance of the mle.
d. Is the mle an efficient estimator? Explain.
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To estimate the mean 1 of the exponential distribution based on a random sample X1 X2 Xn we can foll...View the full answer
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Related Book For 
Modern Mathematical Statistics With Applications
ISBN: 9783030551551
3rd Edition
Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton
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