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.