filtering well what can I should start looking at some reorganization here X 0 where does it appear X 0 only appears at the end here so as we look at this summation we can actually move it we can say this is really X 0 summation can happen in the back here so sum over X 0 P X 1 given X 0 p 0 given X 0 P X 0 because as far as X 0 is concerned everything up front is a constant and bringing up a constant up front is fine to do that's just saying multiplying every term with a constant or first summing it all together and then