%                    The University of Queensland
%     School of Information Technology & Electrical Engineering
%     ENGG7302 Advanced Computational Techniques in Engineering

% Plot the joint p.d.f.s of a pair of Gaussian r.v.s

mu = [0, 0]; % zero mean

[x, y] = meshgrid(-2:0.1:2); % create mesh over which to calculate p.d.f.s

Sigma1 = eye(2); % First case, the r.v.s are independent
f1 = exp(-(Sigma1(1,1)*x.^2 + (Sigma1(1,2)+Sigma1(2,1))*x.*y ...
    + Sigma1(2,2)*y.^2)/2) / (2*pi*sqrt(abs(det(Sigma1))));
figure(1);
surf(x,y,f1);
view([-45,70]);

Sigma2 = [1, 0.5; 0.5, 1]; % Second case, the r.v.s have corr. 0.5
f2 = exp(-(Sigma2(1,1)*x.^2 + (Sigma2(1,2)+Sigma2(2,1))*x.*y ...
    + Sigma2(2,2)*y.^2)/2) / (2*pi*sqrt(abs(det(Sigma2))));
figure(2);
surf(x,y,f2);
view([-45,70]);