how to plot the PDF of a random variable

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MAHMOUD ALZIOUD 2018-9-18

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评论： MAHMOUD ALZIOUD 2018-9-19

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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Answer 1

Dimitris Kalogiros 2018-9-18

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https://ww2.mathworks.cn/matlabcentral/answers/419634-how-to-plot-the-pdf-of-a-random-variable#answer_337345

编辑：Dimitris Kalogiros 2018-9-18

在 MATLAB Online 中打开

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');