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

Say I have a $\text{discrete}$ multivariate random variable $X=[X_1,X_2,\ldots,X_n]$, where each $X_i$ is of the same distribution class. Define random variable $Y$ to be the Manhattan distance between two samples of $X$, and define $Z$ to be the 'normal' Euclidean distance.

Obviously, $Y$ and $Z$ are positively correlated. Given the parameters of the distribution of $X$, is it possible to express this correlation? For instance, given $n$ dimensions, let each $X_i$ be an independent Bernoulli with parameter $p_i$.

share|cite|improve this question
Well, for Bernoulli random variables, even in the non-independent case, $Y=Z^2$. This should simplify the computations. – D. Thomine Jul 8 '12 at 20:35

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.