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.

I want to prove that $P(|A+B|>c)\leq P(|A|>c/2)+P(|B|>c/2)$, where $A$ and $B$ are random variables and $c>0$.

share|improve this question
add comment

2 Answers

up vote 1 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|improve this answer
add comment

Yes, it directly follows from the union bound.

share|improve this answer
add comment

Your Answer

 
discard

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.