$X$ and $Z$ are two independent Normal random variables and $k$ is a constant. I am interested in the following conditional expected value $$\mathbb{E}(X|X < k, X +Z > k).$$
My concern is how to take into account the second condition, which involves another random variable. Note that, since both $X$ and $Z$ are Normal random variables, $X +Z$ is also a Normal random variable, which depends on $X$.
Does this figure help? (I assume statistical independence of $X$ and $Y$.)