Let x1xn be iid with pdf fxtheta13theta theta

Let x1,...xn be iid with pdf f(x;theta)=1/(3theta). -theta <x<2theta, zero elsewhere, where theta>0.

a)Find the MLE theta_hat of theta;
b)Is theta_hat a sufficient statistic for theta, why?
c)Is (n+1)theta_hat/n the unique MVUE of theta, why?

Thank you!

Solution

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