Exercise 3.1: Sampling out of a bivariate Normal distribution

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Draw 4000 samples out of a bivariate Normal distribution with mean \(\boldsymbol{\mu} = (10, 20)\) and a covariance matrix of

\begin{align} \mathsf{\Sigma} = \begin{pmatrix} 4 & -2 \\ -2 & 6 \end{pmatrix} \end{align}

using each of the following three methods.

a) Using Numpy.

b) Using Stan’s build-in random number generator (that is, in the generated quantities block).

c) Using Stan’s MCMC sampler.

Make plots of the samples to show they are consistent.