math but actually for uniform it's intuitive is much simpler for uniform you want to maximize mobility of things you saw but it has to be uniform so essentially you look at the farthest out samples and it's a last spot where you assign any probability and everything in between has the same probability so uniform thing that maximize it would be this thing when your highest sample is be your lowest sample as a it with all the mass between a and B and this uniform has to be equal how about gaussians can do the same thing the math