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

My question is probably very basic. Let's consider random variable from this answer. It looks like probability mass function for each $\xi_i$ is 1/3, 1/3, 1/3 at points 1,2,3. So given pdf for these random variables we cannot find for example $P(\xi_1 < \xi_2)$. So pdf does not contain all info about random variable ? Is there an error in my reasoning?

share|cite|improve this question
up vote 2 down vote accepted

The individual (marginal) pdfs for each random variable, as you have noted, do not contain the information needed to calculate $\mathbb P(\xi_1 < \xi_2)$. But the joint pdf, which you can figure out from the definitions of those RVs as given in that answer, does contain all the information about their distributions.

Marginals alone aren't enough, but the joint pdf is.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.