product rule

$$p(\mathbf{x},\mathbf{y})=p(\mathbf{y}\mid \mathbf{x})p(\mathbf{x})=p(\mathbf{x}\mid \mathbf{y})p(\mathbf{y})$$

• $p(\mathbf{x})$: marginal distribution of the first random variable
• $p(\mathbf{y}\mid \mathbf{x})$: conditional distribution of second random variable given first

해석

• The product rule can be interpreted as the fact that every joint distribution of two random variables can be factorized (or product) of two other distributions.

Related

• sum rule, joint probability, conditional probability, Bayes theorem