Expected Value · Difficulty 6/10 · ~40 min
Expected Value & Linearity
- Compute expected value from definitions
- Apply linearity of expectation
- Design indicator variables
Expected value is probability's center of mass — the long-run average of a random quantity. And it obeys one law so powerful it feels illegal: expectations add, *even when the random quantities depend on each other*. Linearity of expectation solves AIME problems that direct computation cannot touch.