Project for Faculty (Gaussian distribution and estimation)

I would much appriciate the correct response and the code that works on Matlab R2018a.

I need help generating normally distributed random vector X = [X1, X2]' with independent components that both have expactancy 0 and variances sigma1^2 and sigma2^2 (it is given, like in concrete values, but for the sake of generality to the code I don't need to specify values). Also, there needs to be N = 10^5 of those.

Let me say that I cannot use mvnpdf and those functions that are implemented in matlab, but only randn, rand, histogram, histcount and when it comes to plotting plot, stem, surf.

I have to divide the surface (x1,x2) into 20x20 elementary surfaces and to experimentaly estimate probability density function f^(x1,x2) into dots that are in the centers of these elementar surfaces. I have to also plot this f^.

[Jon]

This sounds like a homework problem. Once you have tried writing some code if you are still having problems please attach your code and explain what problem you are having with your MATLAB code

[Jovan Krunic]

The problem I am having is as follows.

This thing below is source code. I have commented on the code. I have emphasised the things I can't use. If somebody knows how to do it I would really appreciate it

clear
close all
clc

%% Generating pdf

% paramaters
m1 = 1; s1 = 0.5;
m2 = 0; s2 = 1;
rho = 0.5;
m = [m1 m2];
sigma = [s1^2 rho*s1*s2; rho*s1*s2 s2^2];

% defining meshgrid for the representation of pdf
x1 = -3:0.2:3;
x2 = -3:0.2:3;
[X1, X2] = meshgrid(x1,x2);

% this in particular I cannot use therego this part must be omitted using somekind of 
% very simple examples of randn function
F = mvnpdf([X1(:) X2(:)],m,sigma);

% graphical representation
F = reshape(F,length(x2),length(x1));
surf(x1,x2,F);
xlim([-3 3])
ylim([-3 3])
xlabel('x1'); ylabel('x2'); zlabel('fgv');
view([0 90]) % prikaz 'odozgo'
% view([90 0]) % prikaz po x2 osi
% view([180 0]) % prikaz po x1 osi

%% Generating the instances of random vector

% number of instances
N=1000;

% again I should not use this I have to generate with randn
r = mvnrnd(m,sigma,N);

% graphical representation
figure
plot(r(:,1),r(:,2),'x')
axis([-3 3 -3 3])
xlabel('x1'); ylabel('x2')

[Jovan Krunic]

@Jon

You might be onto sth.

[Walter Roberson]

The "More About" section of the mvnpdf function gives the equation for it.