Homework 5.1: MCMC with Boolean data with Stan (25 pts)

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a) In Problem 4.1, you got 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 your own sampler. Now, draw 1000 samples out of that distribution using Stan and plot the samples. First do it using Stan’s built-in random number generator. Then, do it using Stan’s MCMC sampler.

b) In Problem 4.2 part (c), we asked you to do the problem using Stan for practice. Now it is real! Repeat Problem 4.2, but use Stan to do it. You do not need to do prior predictive checks nor posterior predictive checks for this problem; you may simply acquire the necessary samples.