The convolution of two functions can be thought of as a measure of the overlap of the graphs as one graph is shifted horizontally across the other. Formally, if
and
are functions, the convolution of the two is the function
.
The plot shows
, that is,
shifted by
units, in blue,
in purple, and the product of the two in gold. Thus the gray area is exactly the value of the convolution at
.
If
and
are independent random variables with respective density functions
and
, then the density function of
is the convolution of
and
. Interestingly, the convolution of two Gaussian densities is a Gaussian density.
