Linearity of Expectation Drills
Linearity of expectation drills for expected counts, indicators, dependent events, payoff decomposition, and review practice.
Candidates who overcount distributions instead of adding small expectations.
Drill indicators
Define a small yes-or-no contribution, compute its expectation, then sum across positions, objects, or trials.
Dependent events are allowed
Linearity of expectation does not require independence. This makes it useful for matches, collisions, and without-replacement settings.
Concrete drill
For five dice, define an indicator for each die showing a six. The expected number of sixes is five times 1/6.
Payoff decomposition
Some payoffs can be split into smaller pieces, such as one dollar per success. Add expected contributions instead of enumerating all totals.
Review loop
After each drill, ask whether you defined the indicator clearly and whether the indexing covered every contribution exactly once.
Common mistakes
Candidates often look for the full distribution when the expected count only needs small expected contributions.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.