for every value of x once we're done we sum it all together to know what the bottom is that will normalize it we can apply this repeatedly that the idea we just saw that this becomes Z on given X px given all the previous ones there's nothing specific about Z N and we'll see then we get a product over all Z is given x times prior over X and so now all we need is that sensor model for each sensor given X we multiply probabilities together and we get our posterior distribution okay for the door example we had in this