Originally Posted by

**matheagle** I'm lecturing on suff stats on monday.

The point is that the indicator function is 0 or 1.

It's 1 as long as each X_i is between 0 and theta.

NOW look at the order stats

YOU need to convince yourself that

0<X_1,...., X_n<theta here these are the unordered data

is the same as

0<X_(1)<X_(2)<.....<X_(n)<theta

which is the same as

0<X_(n)<theta

All we need is the largest to be less than theta

Now if theta was a lower value for our rvs instead of an upper bound,

then the smallest order stat would be suff for theta

And in the case of U(a,b)

the smallest and largest order stats are suff for the TWO

parameters, a and b.

ARE you using Wackerly too?

I knew Dennis at Florida and Scheaffer was my chair there.