7 Law of iterated expectations the continuous case

The tutor begins by recapping discrete case's proof for iterated expectations and transitions to continuous variables' integrals. They remind viewers of joint density, marginal density, and conditional density formulas. The tutorial then walks through algebraic proof using law of total probability and iterated expectation, demonstrating how the integral of conditional expectation equals unconditional expectation. It concludes by paralleling discrete case's sum with continuous case's integral for comparison.