--------> Find (see the code) that makes
and the result follows.
Since the are identically distributed, are identically distributed, and hence their expectation is identical. So we have :b. show that and thus is an unbiased estimator of
Now, how to calculate ?
By the law of the unconscious statistician, we have :
You can see that this is more or less the derivative of , except that there is a constant (a constant with respect to x, so it can be in terms of theta).
From a previous calculation (that you would have done),
So now the integral is just
I hope this helps (there are several steps left to be filled by yourself ^^)