Marginal probability and conditional probability

Edge probability ： In the joint probability distribution of a set of variables , The probability distribution of one subset .

Discrete random variables x and y, And know P(x,y). about P(x) Yes ：

Continuous variable , You can use integral instead of summation ：

** Conditional probability ：** The probability of an event occurring when a given other event occurs . Calculate by the following formula ：

The chain rule of conditional probability （chain rule）： Joint probability distribution of any multidimensional random variable , Can be decomposed into the form of conditional probability multiplication with only one variable .

for example ：P(a,b,c) = P(a|b,c)P(b,c)=P(a|b,c)P(b|c)P