# Seeing if estimators are unbiased

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.

$Y_{min}$ is also exponentially distributed with mean parameter $\frac {\theta} {n}$
Therefore, $E[nY_{min}]=n\times\frac {\theta} {n} = \theta$. Similarly, $E[\frac{1}{n}\sum_{i=1}^n Y_i] = \frac{n \theta}{n}=\theta$