With reference to Exercise 10.72, check whether the following estimators are maximum likelihood estimators of : (a)

With reference to Exercise 10.72, check whether the following estimators are maximum likelihood estimators of θ:

(a) 1/2 (Y₁ + Y_n); 

(b) 1/3 (Y₁ + 2Y₂).

In exercise

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

Show that if Y₁ and Y_n 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.

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