Let $\displaystyle f(x; \theta) = \theta e^{- \theta x}$ and $\displaystyle Y = \Sigma X_i$. What function of Y is an unbiased estimator of theta?

So I know the mean of the exponential distirbutions is $\displaystyle \frac{1}{\theta}$

$\displaystyle E(Y) = E(\Sigma X_i) = \frac{n}{\theta}$

therefore $\displaystyle E(nY^{-1}) = \theta $.

Is this correct? Something about it is bothing me, or am I just being paranoid?