TITLE: What is $E(X\mid X>c)$ in terms of $P(X>c)$?
QUESTION [11 upvotes]: What is $E(X\mid X>c)$ in terms of $P(X>c)$?

I've seen conditional probability/expectation before with respect to another random variable but not to the variable itself. How would I go about interpreting this?

REPLY [9 votes]: $$
\mathrm E(X\mid X\gt c)=\frac{\mathrm E(X\cdot\mathbf 1_{X\gt c})}{\mathrm P(X\gt c)}
$$