# Is there a nice way to visualize the convolution of two random variables?

It is easy for me to visualize the distribution of a random variable by drawing its density function.

Suppose I have two independent random variables now. I can plot the densities and visualize how the masses are spread across the real line. How do I visualize the convolution using that -- is there a way to see how those masses move around and get "combined" in the convolution?

• Have you seen this YouTube video about convolution? It cannot get more visual than that! – Xi'an Jan 14 '17 at 13:44

take a look at

https://en.wikipedia.org/wiki/Illustration_of_the_central_limit_theorem

In general, RVs that look very asymmetrical and bizarre converge faster than you can imagine to a normal distribution. This is the Central Limit Theorem in practice.