How to get correct convolution of two random variables (rayleigh distributed)

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JvdS 2021-1-6

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https://ww2.mathworks.cn/matlabcentral/answers/710308-how-to-get-correct-convolution-of-two-random-variables-rayleigh-distributed

I want to perform convolution of the density functions of two random variables X and Y (Rayleigh distributed).

X has sigma=0.45, Y has sigma 0.29 using anonymous function and integral expression.

The result fz is exactly equal to fy, I don't know why. How can I get the correct solution of probability density Z= X+Y?

sigma1 = 0.45;
sigma2 = 0.29;
% make sure Rayleigh distribution is => 0.
fx_fun =@(x) [0*x(x<0) , (x(x>=0)./sigma1^2).*exp(-0.5*(x(x>=0)./sigma1).^2)];
fy_fun =@(y) [0*y(y<0) , (y(y>=0)./sigma2^2).*exp(-0.5*(y(y>=0)./sigma2).^2)];
% Rayleigh distribution of random var X,Y:
step = 0.1;
x= -2:step:3; % random variable X - positive only
y= -2:step:3; % random variable Y - positive only
%% Convolution:
z= y;
fz = zeros(size(y));
for i = 1:length(y)
    fz(i) = integral(@(z) fy_fun(y(i)).*fx_fun(z-y(i)),0,Inf); % probability density of random variable z= x+y   
end