Focused topic

Linearity of Expectation quant interview practice.

Linearity of expectation converts a difficult total into a sum of simpler expected contributions, without requiring independence. The reviewed questions apply this idea to counts of matches, runs, occupied positions, pairwise interactions, and repeated random constructions. Define one indicator or contribution for each potential feature, express the target as their sum, and take expectations term by term. The main modeling challenge is deciding what to count so that every desired object contributes exactly once. Independence matters when multiplying probabilities, but not for the linearity step itself; confusing those facts is a common interview error. Candidates should also exploit symmetry so that many indicators share the same expectation. The resulting method often replaces a complicated distribution with one local probability, while still allowing checks against obvious bounds and small examples.

Reviewed questions

15

Library records

90

Easy

8

Hard