already have a conditional distribution or XT given XT minus 1 and maybe what's indexed by the action maybe there was no actions it doesn't really matter the math is the same all right so now to think about smoothing and compared to filtering let's work out the basics on the board so we'll do this by example rather than having a you know just very general like any kind of horizon problem we'll pick a very specific horizon just horizon 2 so we'll be interested in this up [Music] we'll be interested in the probability