For a with both unknown and n>=2, you have:
Now, the first moment is:
and the second moment is:
So, you have:
solve these two equations simultaneously for to obtain the estimators.
Specify the moment estimators for and for the normal distribution
I've looking over my textbook to see how to do this but all I've found is this:
An alternative form of estimation is accomplished through the method of moments. The method involves equating the population mean and variance to the corresponding sample mean and sample variance and solving for the parameter, the result being the moment estimator.
There are no examples or anything, so I'm not sure of what to do. I've tried looking online but haven't had luck finding any examples that I understand.
Thanks for the response. After some reading, I get what you're doing. But to reemphasize:
To get moment 1 I do:
And for moment 2 I do:
If this is correct, my only problems left are how to go about integrating these and a strategy for simultaneously solving the resulting equations for and
I kind find the resulting functions for the first and second moment all over the Internet, but I can't seem to find any instructions actually computing the integrals to get to those functions.