
Estimators...
Hello,
Okay, I don't know at all if I did these questions correctly...
Let
and where
Let X be a rv with pdf f.
We know that
Let be a sample of iid rvs following the same distribution as X.
Let the rv and let
Preliminary questions : we proved that Y/n is an unbiased and convergent estimator for .
We also proved that Y follows a binomial distribution with parameter
First question : calculate an estimator T for by the method of moments.

So for this one, ... We know that
So we can take , right ?
I thought of using observations of but then there is a table of values for , not . So I considered it was too easy...

Second question : prove that T converges in probability to and calculate its bias

So in order to prove that it converges, I used the LLN (the one stating the convergence in probability), then used Slutsky's theorem.
Then for its bias, I find 0... is it normal ?? This is where I am the most doubtful...

My own questions :
 is the estimator by the method of moments unique ?
 is it always an unbiased estimator ?
it may sound stupid, but I don't know how to be sure...
Thanks in advance !

do you mean consistent estimator for http://www.mathhelpforum.com/mathhe...c89127591.gif?
And f(x)= 0 for x<1 too
Your mean of X is correct.
But I would think that the MOM estimator of theta would be the solution to
You're using the Z's when you use that Y, those are the truncated X's.
I'm just setting the population mean of the X's to IT's sample mean.
Since

IF you want to use the Y in the MOM estimation, you should set
Now
In that case you get