Calculating expected values: $\mathbb{E}\{ X \vert Y > y \}$ Assuming I know the conditional expected value of the form $\mathbb{E}\{ X \vert Y=y \}$, how do I calculate $\mathbb{E}\{ X \vert Y >y \}$?

Nice question.
Here's how.
$$E(X|Y>y) = \frac{E\bigl( X I(Y>y) \bigr)}{\Pr(Y>y)},
$$
where $I$ is the indicator function, i.e. $I(Y>y)$ equals one if $Y>y$ and zero otherwise.  The numerator is 
$$\int_y^\infty \int_{-\infty}^\infty x dF(x|y) dF(y) = \int_y^\infty E(X|Y=y) dF(y),$$
which simplifies to 
$$\int_y^\infty E(X|Y=y) f(y) dy,$$
if $Y$ is continuously distributed and
$$\sum_j I(y_j>y) P(Y=y_j) E(X|Y=y_j),$$
if $Y$ is discretely distributed with possible outcomes $y_1,y_2,\dots.$
Hope this helps.
