# Sufficient statistics

1. Jan 18, 2013

### abeliando

1. The problem statement, all variables and given/known data
Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.

2. Relevant equations

3. The attempt at a solution
In the attachment.

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• ###### t89M7Rg.png
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2. Jan 19, 2013

### hikaru1221

I think you're into too much math. The I(.) function, if I get its meaning correctly, is nothing but to indicate that it is impossible to sample $x\leq\mu$. With frequentists' approach, this means a lot: you can safely ignore the bunch of I(.)'s and consider only those samples greater than $\mu$. This should solve the problem

3. Jan 19, 2013

### Ray Vickson

Ignoring the fancy notation, what you have for given, fixed μ is that Y = X-μ is exponentially distributed with unknown mean, and you are trying to estimate that mean. You are being asked to show some property of the "usual" estimate.