This web page contains the definition of expected value for discrete and continuous random variables. It also defines moments and conditional expected value. It contains properties, with proofs, of the expected value: the change of variables theorem; linearity; independence; etc. It also contains a discussion of Jensenâs inequality. It also has discussions about expected value for special distributions, some of these are given, some the reader is asked to find (answers are given through a small link at the end of the page). It contains links to simulators and directions for the student to use the simulator to observe various properties.