random number of two random varibles.

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eden meirovich on 28 Apr 2021
Commented: Jeff Miller on 28 Apr 2021
i have 2 random varibles, w and T. they both a ranom varibles of 2 varibles a density function ( f(,w,T)).
is there a way to create a number like rand for this case? i have 2 cases:
where w and T are both uniform disturbiution and where they both gaussian (and might have corelation)
Thank you

Image Analyst on 28 Apr 2021
Did you see the rand() and randn() functions?
w = rand(1, 10000);
T = rand(1, 10000);
w = theMean + stDev * randn(1, 1000);
T = theMean + stDev * randn(1, 1000);
Not sure how to correlate the w with T, but there's probably an option or function for doing that.

Bruno Luong on 28 Apr 2021
Edited: Bruno Luong on 28 Apr 2021
If K is the (2 x 2) covariariance matrix of (w,T) and mu (2 x 1) is the mean of (w,T), you can generate them like this
n = 1000; % number of samples
L = chol(K);
X = mu + L'*randn(2,n);
w = X(1,:)
T = X(2,:)
Jeff Miller on 28 Apr 2021
This is for the case of two normals. For the case of two correlated uniforms, you could adapt the method given in response to this question.