# The formula for conditional expectation in terms of joint cdf


$$P[Y So, $$E[Y|X
• We are assuming that $Y$ has positive support here, right? – AnonA Jan 29 at 12:20
• In the first step, the conditional distribution of Y given X<a needs to have positive support. If the distribution of Y given X<a has support that is bounded below by -M where M is a positive number, then it can still work with some easy modification since Y+M now has positive support and $E[Y|X<a]=-M+E[Y+M|X<a]$. – John L Jan 29 at 18:00