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

I want to prove the estimate

\begin{equation*} P(|A+B|>c)\leq P(|A|>c/2)+P(|B|>c/2), \end{equation*}

where $A$ and $B$ are random variables and $c>0$. Can anyone help?

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

Hint: Use the following: If $|A|\leq c/2$ and $|B|\leq c/2$, then $|A+B|\leq c$. It might be useful to negate this statement and then use the subadditivity of the probability measure.

share|cite|improve this answer

Yes, it directly follows from the union bound.

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.