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
.
