how to plot the PDF of a random variable

2018 9 18
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更新时间：2018 9 19
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Dear All, I have CDF from which I derived the marginal PDF, how can I please plot this pdf which is called here MarginalPDFx?
syms x y
Fxy = 1-exp(-x)-exp(-y)+exp(-(x+y+x*y)); %Given CDF of X & Y
JPDFxy = (x+y+x*y)*exp(-(x+y+x*y)); %Calculated Joint PDF of X & Y
MarginalPDFx = int(JPDFxy,y,0,inf); %Formula for Marginal PDF of X
MarginalPDFy = int(JPDFxy,x,0,inf); %Formula for Marginal PDF of Y

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Dimitris Kalogiros
Dimitris Kalogiros 2018-9-18
编辑：Dimitris Kalogiros 2018-9-18

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From the integral that you use in order to calculate marginal PDFs, I guess that x,y are into the interval [0, +inf].
clearvars; clc; close all;
syms x y
Fxy(x,y) = 1-exp(-x)-exp(-y)+exp(-(x+y+x*y)); %Given CDF of X & Y
JPDFxy(x,y) = (x+y+x*y)*exp(-(x+y+x*y)); %Calculated Joint PDF of X & Y
MarginalPDFx(x) = int(JPDFxy,y,0,inf) %Formula for Marginal PDF of X
MarginalPDFy(y) = int(JPDFxy,x,0,inf) %Formula for Marginal PDF of Y
r=0:0.1:10; %plot PDFs for 0<x,y<10
pdfx=zeros(size(r));
pdfy=zeros(size(r));
for n=1:length(r)
pdfx(n)=MarginalPDFx(r(n));
pdfy(n)=MarginalPDFy(r(n));
end
figure;
subplot(2,1,1); plot(r,pdfx,'-b'); grid on; legend('PDFx');
subplot(2,1,2); plot(r,pdfy,'-r'); grid on; legend('PDFy');
Since Fxy is symmetrical, two PDFs are indentical:

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