TODO
This section goes over visualizing some common operations on probability distributions
Consider the distribution $p(x, y)$. Recall the definition of conditioning $p$ on $x$:
$$ \begin{align*} p(y | x) &= \frac{p(x,y)}{\int_{x \in \mathcal{X}} p(x, y)} \\ &= \frac{p(x,y)}{p(x)} \end{align*} $$
This rescales $p(x, y)$ over the values of $p(x)$, such that $p(y|x = c)$ is a valid probability distribution with some fixed $c$. Choosing a value of $c$ is equivalent to taking a slice of $p(y|x)$ along $x = c$:
