The following proposition stems from the proof of Neyman-Pearson lemma. The result is not quite intuitive, and is there any easier proof?
Proposition 1 Let
are two random variables. Consider
. Suppose there exists
satisfying
then
.
The following proposition stems from the proof of Neyman-Pearson lemma. The result is not quite intuitive, and is there any easier proof?
Proposition 1 Let
are two random variables. Consider
. Suppose there exists
satisfying
then
.