Sums:For X and Y two random variables,
and *Z* their sum, the density of *Z* is

Now if the random variables are independent, the density of their sum is the convolution of their densitites.

Examples:

- 1.
- Sum of two independent uniform random variables:

Now*f*_{Y}(*y*)=1 only in [0,1]

This is zero unless ( ), otherwise it is zero: Case 1:

Case 2: , we have For z smaller than 0 or bigger than 2 the density is zero. This density is triangular. - 2.
- Density of two indendent exponentials with parameter .
,
for
*z*>0