Compare two ad insertion strategies
Company: Meta
Role: Data Scientist
Category: Analytics & Experimentation
Difficulty: medium
Interview Round: Onsite
A feed shows 100 posts. Strategy A: independently turn each post into an ad with probability p = 0.04. Strategy B: deterministically make exactly one out of every 25 posts an ad (i.e., exactly 4 ads, spacing prevents adjacency). For each strategy: (a) Compute E[# ads] and Var[# ads]. (b) Under Strategy A, compute P(# ads ≥ 9) exactly and via a normal approximation with continuity correction; under Strategy B, compute the same probability. (c) Under Strategy A, derive the expected number of adjacent ad pairs and approximate P(at least one adjacent ad) using an appropriate method (e.g., inclusion–exclusion or Poisson approximation). (d) Which strategy is more likely to create back-to-back ads and why?
Quick Answer: This question evaluates a candidate's competency in probability and statistical modeling, including computation of expectation and variance, binomial and normal approximations with continuity correction, Poisson or inclusion–exclusion approximations, and comparison of stochastic versus deterministic experimental designs.