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

Let $X_{1},X_{2},\ldots$ be i.i.d. random variables and let $S_{n}=X_{1}+ \cdots +X_{n}$. Given that $1<a<a'$ and $0<\sigma<\lambda$, how do I show that if $\sup_{1\leq b \leq a'-a}P(|S_{b}|\geq \sigma)\leq \frac{1}{2}$, then $P( \sup_{a\leq b\leq a'} S_{b}\geq \lambda)\leq 2P(S_{a'}\geq \lambda - \sigma)$?

share|cite|improve this question
Please, do not make it look as if you are giving us homework. Show us what you already did and where you got stuck. Also, people will stop answering your questions if you do not accept a single one of them. – sxd Nov 20 '11 at 4:22
Just what Dimitri said. Strongly suggested reading: How-to-ask-a-homework-question. – Did Nov 20 '11 at 9:34

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.