well, you should be a bit paranoid
If then it does not follow that
So, calculate and see what you get.
Let and . What function of Y is an unbiased estimator of theta?
So I know the mean of the exponential distirbutions is
Is this correct? Something about it is bothing me, or am I just being paranoid?
Do as you've been told above : find
In order to do that, recall that , where g is the pdf of Y.
And also see that Y is the sum of n independent rv following an exponential distribution with parameter
So its pdf is the one of a gamma distribution (see here : Exponential distribution - Wikipedia, the free encyclopedia)