How to create two independent Normal distribution ?

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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.
  2 Comments
Masoud Dorvash
Masoud Dorvash on 2 Jan 2021
even with randn I can't be sure that the distributions are independent.

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Accepted Answer

Ive J
Ive J on 2 Jan 2021
Edited: Ive J on 2 Jan 2021
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))

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