IAI May 2011 q9

Hi in this question
I'm not able to get how to take expectation after this step
d2lnf(x)/dtheta2= -1/theta2+2(theta+x)^2

Shouldn't we take expectaion of -1/theta2 also.

As i understood to find CRLB , we need to find L(theta) which is the product till n. Here , they have not taken that and smply started with f(x). Can anyone explain that?

 

Hi

Here X is the random variable and not theta.
NB: E[g(X)]=int[g(x)*f(x)]dx over 0 to inf

You could have taken L(x) = prod over n terms.
Note this equivalent to using log(x) = sum over n terms instead
Hence, Expectation is n times Expectation for one of them

You will see that this has been applied at the CRLB step.

 

Good to see the alternative. Can we get the how to solve it using the traditional method of taking n times. I tried to solve it but it becomes too complex.

 

Yes, you can. It can get complex and you will have to watch your steps.

I always use the simple trick (as below) which always works if you have simple density functions.