clc, clear
% Create three distribution objects with different parameters
pd1 = makedist('Uniform','lower',2,'upper',6);
pd2 = makedist('Uniform','lower',2,'upper',4);
pd3 = makedist('Uniform','lower',5,'upper',6);
% Compute the pdfs
x = -1:.01:9;
pdf1 = pdf(pd1,x);
pdf2 = pdf(pd2,x);
pdf3 = pdf(pd3,x);
% Sum of uniforms
pdf = (pdf1 + pdf2 + pdf3);
% Plot the pdfs
figure;
stairs(x,pdf,'r','LineWidth',2);

pdf = pdf/sum(pdf);

% MATLAB R2018b
pd1 = makedist('Uniform',2,6);
pd2 = makedist('Uniform',2,4);
pd3 = makedist('Uniform',5,6);
a = 0.25;
b = 0.35;
c = 1 - a - b;    % a + b + c = 1

pdfMix =@(x) a.*pdf(pd1,x) + b.*pdf(pd2,x) + c.*pdf(pd3,x);

Xrng = 0:.01:8;
plot(Xrng,pdfMix(Xrng))
xlabel('X')
ylabel('Probability Density Function')

N = 80000;                  % Number of samples
X1 = random(pd1,N,1);       % Generate samples
X2 = random(pd2,N,1);
X3 = random(pd3,N,1);

X = X1 + X2 + X3;           % Convolution