I have the pdf
$$f(y ; \theta) = \frac{1}{\theta} \exp( \frac{-y}{\theta}), \ y > 0$$
and I'm supposed to determine if the following two estimators are unbiased or not: $ \hat \theta = nY_{min} $ and $ \hat \theta = \frac{1}{n}\sum_{i=1}^n Y_i $. I'm running into some problems because when I try to find the expected value of $ Y_{min} $ and $ Y_i $, the integral is undefined.