Quant Interview Expected Value Cheat Sheet
A compact expected value cheat sheet for quant interviews, including direct EV, linearity, indicators, stopping states, fair prices, and risk.
Candidates practicing expected value, betting, and fair-price questions for quant interviews.
Direct expected value
Direct expected value is probability times payoff, summed over outcomes. Use it when outcomes are few and the payoff table is clear. Always define whether you are calculating total payoff, profit, or price.
Linearity of expectation
Linearity says the expectation of a sum is the sum of expectations. It works even when the variables are dependent. This is why indicator variables are so useful for expected counts and matching problems.
Stopping states
If a game stops after a condition, define states and write a recurrence. Expected time recurrences usually include a plus one for the next step. Hitting-probability recurrences usually do not.
Fair prices and bets
A fair price is the expected payoff under the model. A trading decision also needs variance, repeatability, size, and constraints. Positive expected value can still be a poor all-in bet.
Concrete example
For three fair dice, the expected sum is 3 x 3.5 = 10.5. You do not need to enumerate 216 outcomes because linearity makes the sum of expectations enough.
Common mistakes
Candidates over-enumerate, confuse expectation with the most likely outcome, or forget to discuss risk after finding a positive EV. In interviews, explain both the value and the decision it supports.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.