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

Can someone give me an example of two random variables with the same probability distribution but two different density functions? I understand we can do this by changing the density function on a point. Will the value of the distribution function not change due to this. If we make the change does this become a mixed distribution?

share|cite|improve this question
There will be no change. Integrals are insensitive to changes on a "small enough" set. – André Nicolas Dec 18 '12 at 7:23

Try two densities of the same distribution, for example $f=\mathbf 1_{[0,1]}$ and $g=f\cdot\mathbf 1_{\mathbb R\setminus\mathbb Q}$.

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.