Consider the joint distribution function $p(x,y)=p(x) p(y|x)$
$p(x)$ corresponds to the density of a standard normal random variable, whereas $p(y|x)$ is given by $ \frac{1}{2} \delta(y-x)+ \frac{1}{2} \delta(y+x)$
The joint distribution looks like a cross in $\mathbb{R^2}$, where the mass of the standard normal r.v. is located. How can I derive that by my given densities. For fixed $x$ the density of the standard normal is only scaled by $\frac{1}{2} $ for $y=|x|$. Where does then the rotation come from?