# Graphical understanding of the convolution of discrete distributions.

I am studying convolution and trying to get a visual sense of the process. From the wikipedia page I understand what 2 continuous gaussian or 2 uniform distributions will produced when convolved, but I'm having a hard time determine what discrete distributions will look like when convolved. What does the convolution of various discrete distributions look like graphically? Specifically, I'm trying to understand what the histograms of 2 discrete normal and uniform distributions would look like when convolve. Thanks in advance for the help.

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perhaps can be interesting: math.stackexchange.com/questions/255929/… – Seyhmus Güngören Feb 21 '13 at 14:44
Multiply (the base-$10$) numbers $11111111$ by $1111$ by hand, that is, not using a calculator or Mathematica or what have you. That will give you a feel for what the distribution of $X+Y$ looks like if $X$ and $Y$ are independent discrete random variables uniformly distributed on the sets $\{0,1,2,3,4,5,6,7\}$ and $\{0,1,2,3\}$ respectively. – Dilip Sarwate Feb 21 '13 at 14:51
Is the resulting convolution a discrete or continuous distribution? – user1728853 Feb 21 '13 at 14:55
The sum of discrete random variables cannot be a continuous random variable, can it? – Dilip Sarwate Feb 21 '13 at 15:55

It will change almost nothing. You will get the same picture that you got for the continuous case. The idea is the same (shift, multiply,+sum). In the discrete case you have summation instead of integrals. The area under a curve is in the discrete case just the summation of the multiplication of some numbers. Simply same story.

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Perhaps you should see some animation to better understand convolution:

See the continuous first:

http://www-rohan.sdsu.edu/~jiracek/DAGSAW/4.2.html

Then see the discrete:

http://www-rohan.sdsu.edu/~jiracek/DAGSAW/4.3.html

In both you have to click on "play" to let the video play by itself.

and below: