f(y|$\displaystyle \theta$)=$\displaystyle {e}^{[-(-(y-\theta))]}$, y≥$\displaystyle \theta$ where theta is an unknown positive constant.

Find a moment estimator for theta and adjust theta hat to find an unbiased estimator for theta.

Solving for E(Y) I get $\displaystyle y{e}^{y-x}-{e}^{y-x}+{e}^{-x}$ which is my sample average (Y-bar).

Am I on the right track?