Quant Interview Foundations Checklist
A practical checklist for quant interview foundations across probability, expected value, statistics, mental math, coding, and communication.
Candidates checking readiness before moving into mocks or firm-specific prep.
Probability and counting
You should be able to define a sample space, take complements, separate ordered from unordered outcomes, handle replacement, and condition on new information without stopping to think about it. Two self-tests: can you say immediately why two aces off the top of a deck is (4/52) x (3/51) rather than (4/52)^2, and can you explain why "at least one of two children is a girl" makes the both-girls probability 1/3 rather than 1/2? If cards, dice, and coins still feel like unrelated topics instead of three surfaces over the same counting machinery, this foundation is not stable yet.
Expected value and statistics
You should know linearity of expectation and be able to apply it to dependent variables, hold working variance and covariance intuition, recognize the common distributions, and explain sampling error in words. Self-tests: the expected sum of three fair dice is 3 x 3.5 = 10.5 with no enumeration; the expected number of flips to the first head is 2 for a fair coin and 1/p in general; and the variance of a sum of two unit-variance variables with covariance 0.5 is 1 + 1 + 2(0.5) = 3. For trading roles, expected value should connect naturally to fair prices and bet sizing.
Mental math and estimation
You do not need showy speed, but arithmetic has to be reliable enough under pressure that it supports the reasoning instead of derailing it. Fractions, percentages, and common conversions should be automatic: 19 percent as 20 percent minus 1 percent, 48 x 25 as 4800 / 4 = 1200, 1/7 as roughly 14.3 percent. For estimation, you should be able to produce a Fermi answer with stated assumptions and a range rather than a single confident number.
Coding and implementation
For research and developer roles, foundations mean clean loops, the standard data structures, complexity you can state out loud, tests on a small example you constructed yourself, and edge-case handling for empty input, single elements, and ties. Trading candidates benefit from being able to reason through a short simulation even when they will never be asked to write one.
Communication readiness
You should be able to state assumptions unprompted, explain why a method applies, check your own answer, and adjust when the interviewer changes a condition mid-problem. Communication is not polish applied after the math; it is the channel through which the interviewer sees the math at all. A concrete bar: if you cannot explain a problem you have already solved, aloud, in ninety seconds, without notes, it is not yet a foundation.
Common mistakes
A checklist is not permission to delay practice forever. If most items are stable, move into mixed sets and mocks, because the remaining gaps surface faster there than in more review. Conversely, if one item breaks repeatedly, repair it directly instead of stacking harder variants on top of it - harder variants inherit the same broken foundation and simply cost more time to fail.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.