a parameter of probability distribution govern the probabilities associated with different conditions in that distribution. It is usually a vector:

For instance, for uniform \(Uni(\alpha, \beta)\), parameter \(\theta = [\alpha, \beta]\).

importantly, for a discrete distribution system with 6 parameters, we only need 5 independent parameters to be able to satisfy the entire system. This is because a probability distribution must sum to 1.

however, for a conditional probability:

\begin{equation} p(x|a) \end{equation}

we need to specificity \((n-1)m\) parameters, whereby \(m\) is the number of states \(a\) can take, and \(n\) the number of states \(n\) can take. Each group of \(m\) has to add up to \(1\).