Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For a distribution to be factorial : $$P(X) = P(x_1)P(x_2)P(x_3)\cdots P(x_d)$$ My question is :

will $$P(X\mid Y)P(Y\mid Z)$$ be factorial ?

for $P(X\mid Y)$ and $P(Y\mid Z)$ are factorial

Actually the problem I really want to solve is the entropy of the above equation

$$H = \sum_{X,Y}P(X\mid Y)P(Y\mid Z)\log{P(X\mid Y)P(Y\mid Z)}$$

where I know both distribution are factorial, that is

$$P(X\mid Y)=P(X_1\mid Y)P(X_2\mid Y)\cdots P(X_d\mid Y)$$ $$P(Y\mid Z)=P(Y_1\mid Z)P(Y_2\mid Z)\cdots P(Y_d\mid Z)$$

and I am wondering if I can simplify that.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.