Help with unbiased estimators and efficiency

Suppose that Y1, Y2, ..., Yn constitute a random sample from the density function

f(y|t) = e^-(y-t), y>t

where t is an unknown positive constant

a. Find an estimator t1(hat) for t by the method of moments
b. Find an estimator t2(hat) for t by the method of maximum likelihood
c. Adjust t1(hat) and t2(hat) so that they are unbiased. Find the efficiency of the adjusted t1(hat) relative to the adjusted t2(hat)

For part a, I got t1(hat) = Y(bar) - 1
For part b, I got Y(1).....minimum order statistic

If these are correct (let me know please), I still can't figure out how to adjust them so they are unbiased, and I'm not sure how to find the variances to get the efficiency.


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Do you know how to calculate their bias? If you just subtracted off the bias do you think the estimator would still be biased?