random number of two random varibles.

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

Answer 1

[Image Analyst]

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);

Adapt as needed.

Not sure how to correlate the w with T, but there's probably an option or function for doing that.

Answer 2

[Bruno Luong]

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]

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.