# Discrete Convolutions, How to?

1. Mar 13, 2013

### bookworm121

How would you go about convolving two discrete distributions that look something like this:

Number: 0, 1, 2
Probability: 0.1, 0.3, 0.6

Number: 0, 1, 2, 3, 4
Probability: 0.1, 0.3, 0.2, 0.1, 0.3

2. Mar 13, 2013

### Stephen Tashi

The usual kind of convolution computes the probability distribution of the sum of two independent random variables. is that the kind you want? (There is another type of convolution called "circular convolution".)

3. Mar 14, 2013

### HallsofIvy

Staff Emeritus
$\sum_{i= 0}^n f(i) g(n- i)$

Since the second, g, is defined for i= 0, 1, 2, 3, and 4, and the first, f, only for 0, 1, and 2, extend f by setting f(3)= f(4)= 0. f(0)g(4)+ f(1)g(3)+ f(2)g(2)+ f(3)g(1)+ f(4)g(0).