Houjun Liu

joint probability distribution

for random variables \(X, Y\), the joint probability distribution is the probability of both of them happening at once.

\begin{equation} p(x,y) \end{equation}

The most fundamental solution can be derived with a table where all complete probabilities are listed. They are going to be too large to practically store.

probability of the joint of a Bayes Net

\begin{equation} p(joint) = \prod_{i \in BN}^{} p(x_{i} | parents(x_{i})) \end{equation}