and 0 theta equals 0 so now we need to reorganize this a little bit we end up with N 1 minus N 1 theta minus n 0 theta equals 0 so theta equals N 1 over N 0 plus N 1 which is what we hoping for because intuitive result we thought should be the right one but we're covering it in a principled way that does not depend at all on a distribution of this format you can have any kind of distribution and apply the same principle you could say I have a distribution as a complicated functional form very hairy form but I