Question: Let X 1 , X 2 , . . . , X n be a random sample of size n from the uniform population given

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

f(x,e) = 0 elsewhere

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.

f(x,e) = 0 elsewhere

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