Thread: estimator for uniform distribution

Let T be a sample of size s randomly chosen from independent values from a uniform distribution F=F(y,x) on the interval [0,x], and x is not known to us.
is estimator i=T(max) will always be sufficient for i?
is there any way that we can find a unbiased estimator for it
if not how do we prove it?
Thank you

By the factorization theorem the largest order stat, i.e., the maximum of your data set is sufficient for i.
Next find it's density and from that it's expectation.