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I have been tasked with creating 1000 random samples that follow the distribution: $\begin{bmatrix}X_{1}\\X_{2}\end{bmatrix}\sim \mathcal{N} (\begin{bmatrix}3\\1\end{bmatrix}, \begin{bmatrix}7&3\\3&2\end{bmatrix}) $ using Python and Numpy. I have started by generating 1000 random samples 2x1 random vectors with mean 0 and whose covariance matrix is the 2x2 identity matrix using np.random.randn() but now I am not sure how to transform those samples so that they follow the given distribution.

jknut
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    At https://stats.stackexchange.com/a/71303/919 I describe two solutions. More-algebraic explanations can be found by searching [matrix square root](https://stats.stackexchange.com/search?q=matrix+square+root) or [generate multivariate normal](https://stats.stackexchange.com/search?q=generate+multivariate+normal+answers%3A1) – whuber Nov 02 '21 at 13:29

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