I have seen that the sum of $n$ iid multivariate normal vectors (mean $\mu$ and variance $\Sigma$), $X_1+\dots+X_n$, is distributed as a normal with mean $n\mu$ and variance $n\Sigma$. Is the distribution of the average $\frac{X_1+\dots+X_n}{n}$ a multivariate normal with mean $\mu$ and variance $\Sigma/n$?
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1That is right. I think it should be clear to you. It is analogous to how the variance is scaled for univariate distributions. – Michael R. Chernick Jan 20 '19 at 21:42
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@MichaelChernick Thanks, I was just wondering about the covariance elements. Do you know of a reference for this? – multi Jan 20 '19 at 21:43
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1Since covariances are variances of linear combinations, they do not present any additional consideration or problem. – whuber Jan 20 '19 at 22:01