Sufficient Statistics Homework Statement and Solution

[abeliando]

Homework Statement

Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.

Homework Equations

The Attempt at a Solution

In the attachment.

 

[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

 

[Ray Vickson]

Homework Statement

Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.

Homework Equations

The Attempt at a Solution

In the attachment.

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.