I'm trying to understand the intuition behind convolutions for densities Suppose X,Y are RVs and Z = X + Y
then $f_Z(z) = \int_\infty^\infty f(z-y,y)dy$
The lower bound should be negative infinity but I'm having formatting trouble.
Why is this true. By substitution, I feel like this is true: $f_X(x) = \int_\infty^\infty f(z-y,y)dy$
rather than the former