Advanced Statistics Questions
I have two questions:
1) Let X_1, X_2, ..., X_n be i.i.d. from a distribution with pdf:
I am supposed to find the MLE (maxmium likelihood estimator) for theda. However, if I take the derivative of the likelihood function (Likelihood function given below) and set it equal to zero, it doesn't work.
I must maximize the likelihood function a different way then. I argue that in order for the likelihood function to be maximized,
http://img402.imageshack.us/img402/7738/3a3.gif (which is the first order statistic; thus "theda hat" equals the minimum).
Is my logic correct?
2) Let X_1, X_2, ..., X_n be i.i.d. with distribution Laplace(u,1). Find the Fisher information for u.
Here's the pdf:
When I solve the Fisher information, I_n (u), I get zero... is this right? If not, what is another way to solve it?
Thanks for the help!