now say the distribution for XT is XT given XT minus 1 times distribution for XT minus 1 and integrators sum out XT minus 1 and sure we're carrying around all this extra stuff here you want or UT and the Z's and so forth but we know that's just extra stuff we can care around consistently this is just the law of total probability for XT and XT minus 1 then we say well can we simplify this because our mark of assumptions yes we can we don't need to conditioned on everything that's conditioned on there XT given everything in the past only