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Math
Statistics And Probability
fix gt 0 and let x1 ...

Question: fix gt 0 and let x1 ...

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Fix θ > 0 and let X1, . . . , Xn tid. Unif0.θ]. We saw in class that the MLE of θ, θΜLE- max(Xi,... , Xn), is biased. I give two other estimators of θ, which can be made unbiased by appropriate choice of constants C1, C2 1C max(Xi,... ,Xn) and We have two questions (1) Find values of C1, C2 for which these estimators are unbiased. Note that C1, C2 may depend on n (2) Which of these estimators is better? Provide some justification. Note that this question has many possible answers, as there are many ways that one estimator can be better than another. You should supply a reasonable criterion, then figure out which one is better according to this criterion

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