true here I ignored the actions and in principle it could be action everywhere for every time slice but it does not change the math in any way what does the action do the only thing the action does if we're doing estimation is that the conditional distribution of XT plus 1 given X T becomes conditional XT plus 1 given XT and the action but once the action is fixed because you have the whole sequence is just indexing into a conditional distribution and putting it there index by the action and so let's assume that already happened we