Is it possible to find a random vector $(X, Y)$ such that marginal distribution of $X$ and $Y$ are continuous, but the conditional distribution of $X|Y$ (i.e $X$ given $Y$) and that of $Y|X$ are discrete?
I was reading about conditional distributions, and got this doubt? Is there any example for such random variables, or is it impossible to find such random variables ?
Look for questions regarding uncorrelated but not independent normal (a.k.a. Gaussian) random variables here on math.SE or on Wikipedia for examples.