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.

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

Suppose $X$ is a random variable (discrete or continuous) whose values lie in the segment $[0,1]$. Is it safe to say that the standard deviation of $X$ is between $0$ and $\frac{1}{2}$?

share|cite|improve this question
up vote 3 down vote accepted

Yes. $(X-1/2)^2 \le 1/4$, so $$ \text{Var}(X) = \text{Var}(X-1/2) = E[(X-1/2)^2] - (E[X]-1/2)^2 \le 1/4$$

share|cite|improve this answer
Thanks, that's a great and simple solution. – Ron Dec 4 '12 at 9:12

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.