Find min sufficient statistics for a continuous random sample

Let be a random variable from an absolutely continuous distribution with density:

Find the minimum sufficient statistics T and its density.

The solution is as of follows:

Let

Then

, with

I understand that this density gives non zero values only when and but I don't understand how that last line with the two indicator functions come into being. Thank you!

Re: Find min sufficient statistics for a continuous random sample

The suff stat is the max, because it cannot be separated from

that's the factorization theorem in use.

NOW, for your answer.

The marginal densities are ZERO if the X's are not in

HENCE, the joint density is ZERO if all the X's are not in

And, note that

is the same as

is the same as and

YOUR teacher should have had indicator functions on the previous lines as well, let me show you

Re: Find min sufficient statistics for a continuous random sample

Your teacher left out the indicator functions on the first few steps

This should clear it up...

Quote:

Originally Posted by

**tttcomrader** Let

be a random variable from an absolutely continuous distribution with density:

Find the minimum sufficient statistics T and its density.

The solution is as of follows:

Let

Then

, with

I understand that this density gives non zero values only when

and

but I don't understand how that last line with the two indicator functions come into being. Thank you!

Whoever did this doesn't completely understand.

The indicators were there from the beginning.

Sticking them at the end means they don't understand functions as well.