Hello,

(where )

--------> Find (see the code) that makes

Thus

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).

So substitute

From a previous calculation (that you would have done),

And ,

So now the integral is just

And finally

Yay !!!!!!!!!!!!!!

I hope this helps (there are several steps left to be filled by yourself ^^)