# Convolution of two probability density function

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Poulomi Ganguli on 23 Sep 2019
Answered: Jeff Miller on 24 Sep 2019
Hello:
I am interested to add two independent random variables, X1 and X2, described by kernel density functions. Is there any way to find out the joint PDF using convolution process in MATLAB?

Jeff Miller on 24 Sep 2019
I don't know whether you can do this directly in MATLAB. If not, you can do it using the Cupid toolbox. Here is an example:
% Generate some data to use for an example:
data1 = randn(200,1);
data2 = 20*rand(300,1);
% Make the corresponding MATLAB kernel distribution objects:
kern1 = fitdist(data1,'Kernel');
kern2 = fitdist(data2,'Kernel');
% Derive Cupid distribution objects from MATLAB ones:
ckern1 = dMATLABc(kern1);
ckern2 = dMATLABc(kern2);
% Make a Convolution distribution from the Cupid distribution objects:
convkern = Convolution(ckern1,ckern2);
% Compute various properties of the convolution distribution:
a = convkern.Median
b = convkern.Mean
c = convkern.Variance
d = convkern.PDF(12)
e = convkern.CDF(13)
convkern.PlotDens; % Plot PDF and CDF
% et cetera