with the condition of observation given everything else so P Z T plus 1 given X T plus 1 times what we have here P X T plus 1 comma Z 0 through CT now these are bit equations are very easy to run and that's all you need to do to run filtering that's a quick reminder when we go from the joint so here we have the joint when XT plus 1 is e 0 through Z T and here we have a baton ZT plus 1 in general we need to multiply with the conditional of ZT plus 1 given all the variables already present here not just this one variable need to multiply with