If variables with a multivariate normal distribution have covariances that equal zero, then: the correlation will most often be zero, but does not have to be. the marginal distribution of each of the variables is no longer normal: you should use the X2 distribution to calculate probabilities. the variables are independent:

The Normal Distribution

Chapter 4 Multivariate Normal Distribution - SlideServe

Multivariate Distribution: Definition

Bivariate Normal Distribution / Multivariate Normal (Overview)

Consider sampling from a multivariate normal distribution with ... | Filo

Multivariate Experimental Design

Sampling Variability - Definition, Condition and Examples - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day