distribution over state at time two so that's our example in general would be any time T but we're going to do by example for time to given observations at time zero one and two now one thing we know is that this is proportional to the Joint Distribution over x2 and the observation Z 0 Z 1 Z 2 again what does this sign mean the proportional sign what it means is that we're looking at a distribution over x2 and what it means then we can evaluate this quantity here for all values of x2 and once we have all the numbers for every possible value