# Max Likelihood Methods (Estimators)

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Let Y1<Y2<......<Yn be the order statistics of a random sample of size n from the uniform distribution of the continuous type over the closed interval [theta- rho, theta+ rho]. Find the maximum likelihood estimators for theta and rho. Are these two unbiased estimators?

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Please see attachment.

6.4.5 Let Y1<Y2<......<Yn be the order statistics of a random sample of size n from the

uniform distribution of the continuous type over the closed interval [theta- rho, theta+ rho]. Find the maximum likelihood estimators for theta and rho. Are these two unbiased estimators?

Answers:

MLE for theta (Y1+Yn)/2

For rho (Yn-Y1)/2

No

Solution. Since Y1<Y2<......<Yn are the order statistics ...

#### Solution Summary

The expert examines max likelihood methods using estimators.

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