The joint density is
where I is the indicator functions that either 0 or 1.
NOW switch to the order stats and you can factor this as....
So the only stat stuck with theta is our suff stat.
Hi. I really need help with these statistics problem!!
Let be a random sample from a uniform distribution over .
a) Find the joint density and use the Factorization theorem to show is sufficient for .
b) Find the distribution function of and hence show the p.d.f. of is , .
Thanks for your time
c) Find the conditional density ) and show this does not depend on .
d) Show and hence find a function of the sufficient statistic that is an unbiased estimator of .