I would love for someone to review my solution to problem 1( That problem was pretty involved and I’d love to know if there were any shortcuts to take. Finally, without knowing if my calculations are correct, it made comparing the two estimators challenging.

Thanks for any help in advance.

Hi Todd, I think your result for E[theta_hat^2] is incorrect, since theta_hat^2 must be non-negative but your E[theta_hat^2] is negative. Also, the CDF of theta_hat should be (x/theta)^n instead of 1-(x/theta)^n since CDF(x) must be monotonically increasing function in x.