Compare two ad insertion strategies
Overview
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.
Ad Insertion Strategies for a 100-Post Feed
You are evaluating two ad-insertion strategies on a feed with 100 posts:
- Strategy A (Stochastic): Independently convert each post into an ad with probability p = 0.04.
- Strategy B (Deterministic): Insert exactly 1 ad in every block of 25 posts (exactly 4 ads total in 100 posts), with spacing that prevents any two ads from being adjacent.
Answer the following:
(a) Compute the expected number of ads and the variance of the number of ads for each strategy.
(b) Compute P(# ads ≥ 9) under each strategy. For Strategy A, provide both the exact binomial expression and a normal approximation with continuity correction.
(c) Under Strategy A, compute the expected number of adjacent ad pairs (i.e., consecutive ads). Then approximate P(at least one adjacent ad) using a suitable method (e.g., inclusion–exclusion or a Poisson approximation).
(d) Which strategy is more likely to create back-to-back ads, and why?
Solution
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