1 Cholesky Decomposition Correlated Bivariate Normal from IID Random Draws

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Draw two correlated normal shocks using the MVNRND function. Draw two correlated normal shocks from uniform random variables using Cholesky Decomposition.

1.1 Positively Correlated Scores MVNRND

We have English and Math scores, and we draw from a bivariate normal distribution, assuming the two scores are positively correlatd. These are \(x_1\) and \(x_2\).

% mean, and varcov
ar_mu = [70,80];
mt_varcov = [8,5;5,5];
% Generate Scores
rng(123);
N = 10000;
mt_scores = mvnrnd(ar_mu, mt_varcov, N);
% graph
figure();
scatter(mt_scores(:,1), mt_scores(:,2));
ylabel('English Scores');
xlabel('Math Scores')
grid on;