Take the 2-minute tour ×
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.

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space.

If a random variable $X$ satisfies $\mathbb{P}[X<\infty]=1$ (which means $X$ is finite almost surely, doesn't it?) then $\mathbb{E}[X]<\infty$?

share|improve this question
add comment

1 Answer

up vote 4 down vote accepted

No. Take $P(X=2^n)=2^{-n}$. Then $P(X<\infty)=1$ and $E(X)=\infty$.

share|improve this answer
add comment

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.