multiplied with the constant is the same thing then how about X 1 X 1 does not appear in here so we can bring this up front so we can bring P Z 2 given X 2 up front and then we have the summation over X 1 and then this one does have X 1 in it and so that's this one and then this one after we sum out over X 0 we'll have X 1 and Z 0 in it C 0 is a constant that X 1 will be in it so we have to keep it in the back behind this summation now let's give these some meaning and how we would actually run the filtering algorithm