3 - Conditional Probability

Summary of notes from lectures by Sheldon Jacobson for the course IE 410 at UIUC in Fall 2021.

• Definition: Conditional probability, conditional PMF, conditional CDF, conditional expectation.
• Theorem: E(E(X|Y)) = E(X)
• Theorem: Var(X) = E(Var(X|Y)) + Var(E(X|Y))
• Secretary problem
• Theorem: For non-neg continuous randvars, E(X) = ∫_0^∞ P(X>x)dx.