Convolution

The convolution of two functions[Graphics:Images/index_gr_1.gif]and [Graphics:Images/index_gr_2.gif], [Graphics:Images/index_gr_3.gif] is defined to be
[Graphics:Images/index_gr_4.gif]
,which means that the area of the product of two functions becomes the height of the convolution function.

[Graphics:Images/index_gr_5.gif]

Plot of probability density function of both X and Y using "UnitStep" function.

Another ways of finding the convolution is to use Fourier transform and inverse Fourier transform.

Find the Fourier transform of both PDFs.

Find the Inverse Fourier transform of both PDFs to obtain convolution of both PDFs.

Now the plot of the PDF of Z(=X+Y).