2
$\begingroup$

I'm talking with my advisor about how to compute standard deviations for, say, combined standardized test scores for admissions purposes. For example, we'd be interested to compute the sum of the verbal and quantitative scores from the GRE, which are correlated, and normed to be approximately normal.

More formally, say you have a multivariate normal with vector mean and matrix covariance $X \sim N(\mu, \Sigma)$, with $X = (X_1, X_2, ...)$ (and covariances are non-zero). What is the variance of $\sum{X_i}$? If it's hard to compute in general, I'm happy with bivariate for now, a recursive approach or similar.

$\endgroup$
5
$\begingroup$

The variance is the matrix product: $$ 1'\Sigma1 $$

$\endgroup$
  • $\begingroup$ I knew this couldn't be that hard. Note, whuber's link above gives a more general answer. $\endgroup$ – Dav Clark Jun 30 '11 at 3:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.