Calculate Ad Insertion Statistics for Two Methods
Overview
This question evaluates competency in probability and statistical modeling—expectation, variance, tail probabilities, and dependence/clustering in discrete sequences—within the Statistics & Math domain.
Meta
Jul 12, 2025, 6:59 PM
Data Scientist
Onsite
Statistics & Math
65
0
Scenario
Evaluating two ad-insertion strategies in a 100-post feed.
- Option A (independent placement): Each post independently becomes an ad with probability p = 0.04.
- Option B (quota per block): Exactly 1 out of every 25 posts is an ad.
Assumption for Option B: The total ad count is deterministic (4 ads in 100 posts). If positions are not fixed, assume 4 blocks of 25 posts; in each block, the ad’s position is chosen uniformly at random and independently across blocks. If positions are fixed (e.g., every 25th post), call that out where it affects adjacency.
Questions
- For each option, compute the expected number and variance of ads in 100 posts.
- For each option, compute the probability of showing more than twice the expected number of ads.
- For each option, estimate the expected count of adjacent ad pairs (i.e., post i and i+1 both ads) and determine which option is more likely to create long runs of ads.
Hints: Use binomial moments for A, deterministic counts for B, normal tail approximation, and (n−1) p^2 for adjacent-pair expectation.
Solution
Login required
Show