How Do You Convolve Two Discrete Distributions?

[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

 

[Stephen Tashi]

How would you go about convolving two discrete distributions

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".)

 

[HallsofIvy]

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

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).