MATLAB: How to create two independent Normal distribution

Question

I want to create two (or more) independent distributions, then I want to find the Covariance of them.

My problem is how to define two independent distributions.

X = makedist('Normal');
Y = makedist('Normal');
Z = X + Y;

Here, I can't add these two distributions, even I don't know if they are independent or not.

Answer 1

You basically can generate multiple independent normal random variables form a multivariate normal dist. You just need to define var-covar matrix properly. So, to generate two iid vectors, you can generate them from a bivariate normal dist:

mu = [0 0];
Sigma = [1 0; 0 1]; % set off diagonals to zero
X = mvnrnd(mu, Sigma, 1e5);
% visual examination
histogram2(X(:,1), X(:,2))

% are they really independent?
histogram(sum(X, 2))