Hi Giovanni,
I understand that you are facing issues while making a 3 dimensional histogram of a PDF function.
Since you have clearly mentioned that you are facing issues in the implementation of the plot, I am assuming that your calculations are correct. From the problem statement, it seems that you want to plot the histograms of x and y values from the experimental data.
To achieve this, you can use the "hist3" function. You can refer the to the documentation for "hist3"at the following link: https://www.mathworks.com/help/stats/hist3.html.
If you want to plot the rho_xy as well with the histogram, you can use the "surf" function. You can refer the to the documentation for "surf" at the following link: https://www.mathworks.com/help/matlab/ref/surf.html
Note that to show both the plots in the same axes, you need to use "hold on".
I am using random values to show an example:
x = randi(10, 100, 1); %100*1 matrix of random doubles ranging from 0 to 10
y = randi(10, 100, 1);
hist3([x y]);
hold on
arraySize = 100;
sigma = 50;
x1 = linspace(0,10,arraySize); %100 points between 0 to 10
[X,Y] = meshgrid(x1,x1); %setting up for the x and y axis for the surf plot
z = fspecial("gaussian", arraySize, sigma); % gaussian distribution
z = z*(3/max(z,[],'all')); % scaling from 0 to 3
surf(X,Y,z);
hold off
Hope this helps!
