Expected Value
Computational problems involving probability, expected value (in particular linearity of expectation), and Markov chains (processes which move from state to state). A good precursor to the Global unit.
Unit Overview
Expected Value is a computational-heavy unit with very few olympiad problems. It is considered to be one of the easiest units along with Sympoly. It contains one of the most important combinatorics concept - Linearity of Expectation. You also learn about applying Markov Chains to expected value problems (more commonly known as States).
Notable Problems
- NIMO56: Introduces the idea of symmetry.
- HMMT 2018/9: A cool application of planar graphs.
- AIME II 2018/13 : An informative expected value problem.
Advice
This is a very good unit to use for late AIME combinatorics, but it has very few applications to olympiad problems. The only relation is through a middle step, the Global unit, which uses some ideas from this unit and builds upon this unit. It is recommended to do this before Global.
One thing about this unit is that it has no 9-club problems. 18 of the 27 minimum clubs come from required problems. This unit has 35 clubs if you have time, and a maximum of 59.