Re:Random Variable Algebra
by hwita on Saturday July 10, 2021 @11:52PM
(#27798336)
I feel like more explanation is needed between steps 4 and 5 of the proof.
[ Parent
| on HN ]
Visualize it.
You are integrating a function P(X) along a thin surface defined by z<f(X)<z+dz.
What is volume dV for a given dz? It is a surface dS times dX: the amount that X changes for a given dz. Since z=f(x), then dx=dz/|∇f(x)|. So dV=dS*dz/|∇f(x)|