My textbook makes a calculation and just says "with some simplications", and then gets the answer.
We have L0=(1/sqrt(2pi))^n*(e^(-1/2*sum(xi-m0)^2)...i.e. this the max likelihood function for a normal with variance 1 and mean m0. Sum is from 1 to n. We have L1 is the same except replace m0 with m1.
Then they compute L0/L1 and get
I do not see where this step comes from. Any ideas?
Just how they get that form of Lo/L1...I understand the analysis that follows using the Neyman Pearson lemma, but I just don't understand this, and maybe it's an algebraic thing I'm missing, but I don't see how they are getting the e^((n/2)*(m1^2-m0^2)+(m0-m1)*sum(xi)) from the two likelihood functions.....Maybe there is some property of sums I am missing, but I am not sure.