often a assumption is applied to simplify the math is that the sensor measurements are all independent given the state of the world because the state of the world is causing what you measure and so if the state of the world is a known entity then each outcome is independent given that state that will simplify the math because then when we look at Z M the enth sensory measurement given the state of the world X and all the other sensory measurements we don't need to build a model for Z and given X and the other measurements we just need