convolution

n+(m-1)

 0 0 0 1 2 3 0 0 0
 1 2 3 4

(3,6)
(n,n+(m-1))




0  1/6 1/6 1/6 1/6 1/6 1/6

P(X=x){0, x=0}
             {1/6, x=1,2,3,4,5,6}

p(y2=0)=p(x=0)p(x=0)
p(y2=1)=



0 0 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 .....pdf for sum of two dice

z[1]=0 z[2]=0 z[3]=1/36



three dice

0 0 0 1/218