We are taking the indicator function because (this is a consequence of the pdf of X)
For the product (in the joint pdf) to be different from 0, we need
So , which means that the minimum among the 's should be . Hence the result.
Hi, I am preparing for my test. I have a question about sufficient statistics. More to follow later.
The problem has been worked this way:
and thus factorization theorem concludes that is a suff stat for (mu,sigma).
I am conused in why we are taking the indicator function and why was the minmum order statistic used. Could anybody explain? Thank You.
Thanks, and one more thing. If i wanted to know whether the sufficient stat above is also a minimum sufficient what shall I do?
I looked at few examples in the book where two sample points x and y are considered and the ratio of their pdfs are taken, but I am confused on how to use that here. Could you tell?