Bayesian network

Let $G = (V,E)$ be a directed acyclic graph and let $X = (X_v)_{v \in V}$ be a set of random variables. We say $(G,X)$ forms a Bayesian network if the probability density function is given by

$$\mathbb{P}[X] = \prod_{v \in V} \mathbb{P}[X_v \vert \bigcap_{(u,v) \in E} X_u].$$