Probability

Convolution

How the sum of independent random variables produces a new distribution

Flip and slide: $f(x)$ and $g(z - x)$

Result

How it works

$(f * g)(z) = \int f(x) \cdot g(z - x)\, dx$. Flip g, slide it by z, multiply with f, and integrate the overlap.
Uniform + Uniform = Triangle. The overlap area grows linearly then shrinks, forming a triangle.
The green area in the top chart is the integrand at each position. Its total area equals the result value at that z.
Order doesn't matter: $f * g = g * f$. Convolution is commutative.