Focused topic

Expected Value and LOTUS quant interview practice.

Expected value questions test whether a candidate can translate a payoff, count, or stopping rule into a random variable before performing arithmetic. This collection emphasizes the law of the unconscious statistician, indicator decompositions, tail sums, discrete payoff tables, and integrals for continuous variables. Start each problem by defining the quantity being averaged and its support. Then choose the shortest representation: sum over outcomes, integrate against a density, condition on a useful first event, or express a total as a sum of indicators. The exercises also train sanity checks involving units, symmetry, bounds, and limiting behavior. LOTUS is most useful when the distribution of a transformed variable would be awkward to derive directly. The broader goal is not formula recall, but selecting a representation that makes the expectation transparent and defensible in an interview.

Reviewed questions

48

Library records

454

Easy

25

Hard