multiplied and dynamics some out over the past state variable and repeat so we have a general recursive approach to finding these things and let's see we're going to put this let me put it over here we have P XT plus 1 comma Z 0 through ZT is equal to sum over X T the dynamics model XT plus 1 given X T times X T comma Z 0 through CT and then to bring in that last observation ZT plus 1 which is ultimate what we want here for that update now we have Z 0 through Z T n ZT plus is going to be multiplying this thing