joint the fool joint would be Z 4 given X 4 that's happening all the way at the end then X for given X 3 then Z 3 given X 3 x3 given X to Z 2 given X 2 and it will continue on this other board X 2 given X 1 the C 1 given X 1 X 1 given X 0 z 0 given X 0 and then the prior P X 0 this is the full joint now for this full joint we know we don't care about X 0 X 1 X 3 and X 4 so we're going to sum them out to get rid of them X 0 X 1 X 3 X 4 we sum out over to get this quantity over here alright now we're going to play the same trick it's during when we