Here's the setup:

I need to find
a) MLE of \theta
b) Unbiased Estimator of \theta
c) Compare a) and b)

for X ~ Unif(\theta - 1, \theta + 1)

Work:

a) MLE

My first idea was to consider Y = |X|. Then the MLE would be max(Y)

But then I found this post:
http://www.mathhelpforum.com/math-he...estimator.html

So now I'm leaning towards using [x_(1) + x_(n)] /2.

b) Unbiased.

No ideas here...