I spent the first day of 2026 revisiting the concept of Conditional Expectation.
It’s fascinating how a concept often introduced as “just a formula” in introductory probability courses reveals its true geometric nature when viewed through the lens of Hilbert spaces. The note on Conditional Expectation has been updated to reflect this perspective—moving away from mechanical definitions towards the intuition of orthogonal projections.
Sometimes, rewriting a note is the best way to verify if you truly understand something.