Probabilities for a single variable

A model for two categorical variables is characterised by the joint probabilities pxy.

The marginal probability, px, for a variable X is the proportion of (xy) pairs in the population with X  = x . This can be found by adding all joint probabilities for pairs with this x-value.

There is a similar formula for the marginal probabilities of the other variable,

Example

In the following example, the marginal probabilities for X are the row of totals under the table, and the marginal probabilities for Y are the column of totals on the right.

Joint probabilities
  Variable X  
Variable Y X = A X = B X = C Total
Y = 1 0.2576 0.1364 0.1212 0.5152
Y = 2 0.0909 0.0758 0.0152 0.1818
Y = 3 0.0455 0.0758 0.0606 0.1818
Y = 4 0.0152 0.0303 0.0758 0.1212
Total 0.4091 0.3182 0.2727 1.0000