Problem with noisy gaussian function

Hello everyone ,

I'm student(from France). This is the problem : "Create a noisy gaussian function using the Matlab built-in function rand . You'll first check what rand is doing using help rand. The idea will be to create random-numbers having a mean value zero(i.e positive and negative numbers)."

I did for help rand . It's an array but I didn't understand how can i create this function . If you have clue or some advice . Thanks you very much .

Answer 1

[Dimitris Kalogiros]

You must use Central Limit Theorem

Bellow is an rough attempt of mine:

 clearvars; clc; close all;

%%parameters

N=2^16; % rand() outputs
M=2^7;  % number of rand that we will use

%%uniformly distributed random numbers  

x1=rand(1,N)-0.5;

% probability density function
h1=histogram(x1);
h1.Normalization = 'probability';
title('uniform distribution')

%%combination of M rand() functions

x2=zeros(1,N);
for k=1:M
    x2=x2+rand(1,N)-0.5;
end

%probability density function
h2=histogram(x2);
h2.Normalization = 'probability';
h2.FaceColor=[0 .5 0];
title('Normal distribution');

If you run this script, you will receive :