Let denote a random sample from the uniform distribution on the interval . Let
and
a) show that both and are unbiased estimators for
b) show that both and are consistent estimators for
Attempt
a) I figure simplifying I get:
so for the estimator of
I know I'm near the end for but I don't know how to get it into to above form.
for which is an order stat. my , thus for the max function which is , so getting the estimator:
at this point I get stuck.
b) Looking at the definition
so for
thus
this next step I'm not sure, but it looks similar to the example I have in the book at which point I don't know how to proceed.
for
for the variance
I can't seem to go further from here.