Originally Posted by

**romsek** The trouble that I have with this is that $Pr[X+Y=1]=0$.

The loci of points in the X,Y plane where this is true is a 1D line of zero 2D measure.

The probability of these points is the 2D integral 2D standard normal distribution along this line and this integral is 0.

So I don't see how to obtain a non-zero distribution of $p(X | X+Y=1)$

My intuition says that something conditioned on something impossible (of probability 0) can never happen and is thus also probability 0.

What might be instructive is to let $1-\epsilon <= X+Y <= 1+\epsilon$, find the marginal of X given that, now possible, condition, do the math from there and see what happens in the limit as $\epsilon \to 0$

This could all be incorrect and maybe one of the powerhouses will chime in with some wisdom.