# Unnormalized multivariate Gaussian?

#### dbooksta

##### New Member
I'm looking at bivariate Gaussian variables centered on zero.

The chi distribution provides moments for a normalized multivariate Gaussian -- i.e., a random variable $$Y = \sqrt{\sum (\frac{X_i}{\sigma_i}})^2$$.

But I want the variance for the unnormalized vectors $$Y' = \sqrt{\sum X_i^2}$$, so I can see the relationship with the constituent variances.

Is there a canonical distribution for that? If not how can we derive that unnormalized variance?