In [[statistics]], the '''Conditionalconditional Probabilityprobability Table'''table (CPT)''' is defined for a set of discrete (not independent) [[random variable]]s to demonstrate [[marginal probability]] of a single variable with respect to the others. For example, assume there are three random variables <math>x_1,x_2, x_3</math> where each have <math>K</math> states. Then, the conditional probability table of <math>x_1</math> provides the marginal probability math values for <math>P(x_1|\mid x_2,x_3)</math>. Clearly, this table has ''K''<mathsup>O(K^3)</mathsup> number of rowscells. In general, for <math>M</math> number of variables <math>x_1,x_2,...\ldots,x_M</math> with <math>K</math> states, the CPT has the size of ''K''<mathsup>O(K^''M)''</mathsup>.<ref name=murphybook /><ref>{{cite book|last=Murphy|first=KP|title=Machine learning: a probabilistic perspective|year=2012|publisher=The MIT Press}}</ref>
CPT table can be put into a matrix form. For example, the values of <math>P(x_j|\mid x_i)=T_{ij}</math> create a matrix. This matrix is [[Stochasticstochastic matrix]] since its row sum is equals to 1; i.e. <math>\sum_j T_{ij}</math>.
