In statistics, the conditional probability table (CPT) is defined for a set of discrete (not independent) random variables to demonstrate marginal probability of a single variable with respect to the others. For example, assume there are three random variables x 1 , x 2 , x 3 where each have K states. Then, the conditional probability table of x 1 provides the marginal probability values for P ( x 1 ∣ x 2 , x 3 ) . Clearly, this table has K3 cells. In general, for M number of variables x 1 , x 2 , … , x M with K states, the CPT has size KM.
CPT table can be put into a matrix form. For example, the values of P ( x j ∣ x i ) = T i j create a matrix. This matrix is a stochastic matrix since sum of all its elements is equals to 1; i.e. ∑ j T i j .
