Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

I have two discrete random variables $X$ and $Y$, let $P_X$ and $P_Y$ be the PMF of the random variables, if $Y=X^2$ ,I want to know the PMF of Y in terms of PMF of X ?

I know how to do it with continuous RVs


is there a difference if X and Y are discrete RVs?

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

If the random variables are discrete, then the probability mass function is given as follows. $$\mathbb{P}_Y(Y = y) = \mathbb{P}_X(X^2 = y) = \begin{cases} \mathbb{P}_X(X = 0) & \text{ if }y=0\\ \mathbb{P}_X \left(X = \sqrt{y} \right) + \mathbb{P}_X \left(X = -\sqrt{y} \right) & \text{ for all }y > 0 \end{cases}$$

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.