conditional expectation

(1.8 hours to learn)


The conditional expectation E[X | Y] is the expectation of X in the conditional distribution P(X | Y).


This concept has the prerequisites:


  • Know the definitions of conditional expectation for both discrete and continuous random variables
  • Know and be able to apply the law of iterated expectations

Core resources (read/watch one of the following)


See also

  • Some uses of iterated expectations:
    • they justify the use of Monte Carlo estimators
    • they are used in the definition of martingales