Expected Value in Algorithms — Analyzing Random Behavior

Why it matters

Analyzing randomized algorithms requires expected value. Understanding enables rigorous analysis.

The architecture

E[X] = sum of x × P(X = x).

Linearity: E[X + Y] = E[X] + E[Y]. Even for dependent variables.

How it works end to end

Indicator variables: 1 if event happens, 0 else. Sum + linearity gives count.

Chernoff / Hoeffding: concentration bounds. Deviation from expectation with high probability.