What exactly does $X_1,...,X_n$ mean in $X_1,...,X_n \sim N_p(0,\Sigma)$ (iid) ?

I am confused, since what I imagine is that the variables $X_1,...,X_n$ are the columns of a dataset? But From the fact that $N_p$ has index $p$, there are only $p$ variables and hence columns.

So, are $X_1,...,X_n$ rows? Are they datasets each containing $p$ variables/columns?


1 Answer 1


The $X_i$'s are independent random Gaussian vectors, each $X_i$ being of dimension $p$. Once observed, they can be stored as an $n \times p$ matrix but this does not help with their mathematical definition.

  • $\begingroup$ So the dataset consists of n columns and p rows? $\endgroup$
    – user274779
    Jan 13, 2021 at 9:58
  • $\begingroup$ @Marina N rows and p columns. $\endgroup$ Jan 13, 2021 at 11:08
  • 2
    $\begingroup$ It could be either, it is a matter of convention. $\endgroup$
    – Xi'an
    Jan 13, 2021 at 12:00

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