# Question

Let X1, X2, . . . , Xn be a random sample of size n from the uniform population given by

Show that if Y1 and Yn are the first and nth order statistic, any estimator Θ such that

Can serve as a maximum likelihood estimator of θ. This shows that maximum likelihood estimators need not be unique.

Show that if Y1 and Yn are the first and nth order statistic, any estimator Θ such that

Can serve as a maximum likelihood estimator of θ. This shows that maximum likelihood estimators need not be unique.

## Answer to relevant Questions

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