# Maximum likelihood and Fisher information

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Suppose x(sub 1), x(sub 2), ..., x(sub n) is a random sample from a distribution with probability density

f(x/ÃŽ?)=( 1 / (ÃŽ?+1)) e^(-x/(ÃŽ?+1) where x>0 and ÃŽ?> -1

A. Find the maximum likelihood estimator of ÃŽ? and show it is unbiased.

B. Find the Fisher Information I(ÃŽ?).

C. Does the variance of the maximum likelihood estimator attain the Cramer-Rao lower bound?

https://brainmass.com/statistics/maximum-likelihood-estimation/maximum-likelihood-fisher-information-315418

#### Solution Summary

Suppose x(sub 1), x(sub 2), ..., x(sub n) is a random sample from a distribution with probability density

f(x/ÃŽ?)=( 1 / (ÃŽ?+1)) e^(-x/(ÃŽ?+1) where x>0 and ÃŽ?> -1

A. Find the maximum likelihood estimator of ÃŽ? and show it is unbiased.

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