Evaluates ad-insertion load under 4% random replacement versus fixed one-in-25 scheduling. Strong answers compute expected counts, variance, overload probability, and compare variability, pacing, and user experience.
Scenario: Team A wants 4 % random replacement; Team B prefers a fixed 1‑in‑25 slot. Compare expected ad counts, variance, and risk of overload.
Question 1: Compare two insertion methods—4 % random vs 1‑in‑25 fixed—calculate expectation, variance, and chance of exceeding twice expectation. (Hint: binomial distribution, load smoothing)
Quick Answer: Evaluates ad-insertion load under 4% random replacement versus fixed one-in-25 scheduling. Strong answers compute expected counts, variance, overload probability, and compare variability, pacing, and user experience.
You are designing an ad insertion system. In a short time bucket or session, there are n eligible content slots where an ad could be inserted.
Two teams propose policies:
Team A: replace each slot independently with probability p = 0.04.
Team B: use a fixed periodic schedule of exactly one ad every 25 slots.
Assume buckets are contiguous sequences of n slots; when relevant, assume the starting phase of the fixed schedule is uniformly random across the 25 positions.
Constraints & Assumptions
Compare ad count in a bucket of n eligible slots.
For fixed scheduling, account for bucket alignment with the 25-slot period.
Include expected count, variance, overload probability, and product interpretation.
Overload means the number of ads exceeds twice its expectation.
Clarifying Questions to Ask Guidance
Are buckets aligned to session boundaries, time windows, or content slots?
Is the fixed schedule phase randomized across users or sessions?
Are there additional ad-spacing rules or frequency caps?
Is the goal expected load, pacing, or tail-risk control?
Part 1 - Expected Count and Variance
For each method, compute expected number of ads and variance in n slots.
What This Part Should Cover Guidance
Model Team A as Binomial(n, 0.04).
For Team B, write n = 25q + r and account for q or q+1 ads depending on phase.
Show that expected counts are comparable at n/25.
Explain variance differences.
Part 2 - Overload Probability
For each method, compute or bound the probability that ad count exceeds twice expectation.
What This Part Should Cover Guidance
Use binomial tail probability or Chernoff/normal/Poisson approximation for Team A.
For Team B, use the deterministic or phase-randomized count structure to bound overload.
Explain when overload is impossible or very unlikely.
Part 3 - Product Comparison
Compare the methods in expected counts, load smoothing, and overload risk.
What This Part Should Cover Guidance
Team A is simple and randomized but has higher variance and clustering risk.
Team B smooths load but can be predictable and has boundary effects.
Connect to user experience, advertiser delivery, experimentation, and fairness.
Follow-up Questions Guidance
What if users view fewer than 25 slots?
How would you test user experience under both methods?