Y to the next time X then this equation will tell something about the joint and hence tell us something about X then if x and y are independent then the conditional of X given Y is the same as the marginal for X so P of X will call the Marshal for X and so that means that sometimes in our math we'll be able to simplify things you have an assumption X in planet of Y we see X given Y appear we can just get rid of the Y and simplify to just px all of this is also true for probability densities it's just in densities often it's a small P but