Conditional probability table

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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 ${\displaystyle x_{1},x_{2},x_{3}}$ where each have ${\displaystyle K}$ states. Then, the conditional probability table of ${\displaystyle x_{1}}$ provides the marginal probability values for ${\displaystyle P(x_{1}\mid x_{2},x_{3})}$. Clearly, this table has ${\displaystyle K^{3}}$ cells. In general, for ${\displaystyle M}$ number of variables ${\displaystyle x_{1},x_{2},\ldots ,x_{M}}$ with ${\displaystyle K}$ states, the CPT has size ${\displaystyle K^{M}}$.

CPT table can be put into a matrix form. For example, the values of ${\displaystyle P(x_{j}\mid x_{i})=T_{ij}}$ create a matrix. This matrix is a stochastic matrix since the rows sum to 1; i.e. ${\displaystyle \sum _{j}T_{ij}=1}$.

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Source of the article : Wikipedia