How Do You Calculate the Cramer-Rao Lower Bound for θ?

[Sander1337]

Hi there,

I've got a distribution function for an assignment for my school here and I don't get the hang of the question;

f(x) = θ* 2^θ * x^(-θ-1) for x>2
0 for else

The assignment is to calculate the Cramer-Rao lower boundary for consistent estimators of θ.

This is what we've got so far;

Cramer-Rao lower boundary:
[-n*E[d^2/dθ^2 ln(f(y))]]^-1

(d^2/dθ^2)ln(f(x)) = -θ^(-2)= CRLB function

Now since our professor didn't explain the Cramer Rao lower boundary we haven't got a clue of how to continue now. Is there someone here who knows how to continue now?

Greetings,

Tony, Siebe & Sander

(question might be in wrong (sub)forum, apoligies for that, don't bother rerouting this question to the right (sub)forum, thanks!)

 

[mXSCNT]

Well, the next step is to take the expected value (with respect to x). Since -θ^(-2) does not involve x, it is just a constant, so the expected value is -θ^(-2) itself.