What is Neyman-Pearson lemma? Why is this proof of Neyman-Pearson's lemma look so diffcult? What is Neyman-Pearson lemma? Why is this proof of Neyman-Pearson's lemma look so diffcult? I am consider taking a undergraduate course in my college called mathematics of statistics and in the course description, a term comes up and it look so difficult to me. What is a book that including a proof that is easy to read? Please including an alternative proof that is easier if you want to! Appreciate in advance. !enter image description here

Problem 12 at this URL gives a proof of the Neyman--Pearson lemma. Maybe you'll find that more comprehensible. (Or maybe not?)

At any rate, the lemma says that for testing a point null hypothesis versus a point alternative, the likelihood ratio test is the unique most powerful test at any particular level (i.e. any particular tolerated probability of Type I error).