This was the warmup and I almost overthought it.
First, clarify the ad insertion methods and assumptions (e.g., fixed interval, dynamic, etc.). Then, for each method, calculate the expected number of ads per 100 posts using simple arithmetic or probability, and discuss factors that could affect the actual count.
Pro tip: Acknowledge that real-world ad load is often capped and optimized for user experience, so the theoretical maximum may not be reached. Mention that you would validate with A/B tests or historical data.
Ask the interviewer to specify the ad insertion methods (e.g., every N posts, after specific content types, etc.) and any constraints (e.g., max ads per session).
State assumptions such as no ad fatigue, consistent insertion rules, and that each ad slot is filled. For example, if ads are inserted every 5 posts, then 100 posts yield 20 ads.
For each method, compute the expected number of ads. For fixed interval: ads = floor(100 / N) or ceil depending on placement. For probabilistic: ads = 100 * p, where p is probability of ad after each post.
Consider factors like ad caps, user engagement, and dynamic insertion that may reduce the actual number. Mention that the expected value might be lower due to these constraints.
Provide a concise summary of expected ads for each method, highlighting which yields more ads and why. Suggest how to validate with data.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the two ad-serving methods and the underlying probabilistic model (e.g., Poisson or binomial) for ad exposure. Then compute the probability that a user sees more than twice the expected number of ads for each method, and compare these tail probabilities to assess which method has a heavier tail.
Pro tip: Always state your assumptions about the distribution and independence of ad views; in practice, ad views are often overdispersed, so a Poisson model may underestimate tail risk—mentioning this shows depth.
Identify the two methods, the expected number of ads per user for each, and the assumed distribution (e.g., Poisson, binomial, negative binomial). Confirm whether 'expected number' refers to the mean of that distribution.
For each method, let X be the number of ads a user sees. The event is X > 2 * E[X]. Write the probability as P(X > 2μ) where μ = E[X].
If X ~ Poisson(μ), compute P(X > 2μ) using the Poisson CDF or a normal approximation with continuity correction. For other distributions, use the appropriate formula or simulation.
Compare the computed probabilities for the two methods. Discuss which method has a higher chance of extreme ad exposure and why (e.g., difference in μ or distribution shape).
Relate the results to product metrics: heavier tails may indicate user experience risks or targeting inefficiencies. Suggest potential follow-up analyses or metric adjustments.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Method A can theoretically cluster ads anywhere since each post is independently replaced.
First, clarify the two insertion methods and define what 'consecutive ads' means in the context of the product. Then, compare the likelihood of consecutive ads for each method and explain how the maximum streak length would differ, using probabilistic reasoning and considering user behavior.
Pro tip: Ground your answer in a concrete example, such as ad insertion in a feed, and discuss how the method affects user experience and metrics like ad load and user engagement. This shows you can connect technical details to business impact.
Identify and define the two insertion methods being compared, such as random insertion versus deterministic insertion based on position or time.
Specify what constitutes consecutive ads (e.g., ads appearing back-to-back in a sequence) and how this relates to the insertion method.
For each method, reason about the probability of consecutive ads occurring, considering factors like insertion frequency and independence.
Explain how the maximum possible streak of consecutive ads differs between methods, e.g., due to constraints or randomness.
Discuss how these differences impact user experience, ad performance, and overall product metrics, showing awareness of trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Went with complement approach for Method A: probability of no consecutive ads is harder to compute exactly so I flagged that and gave a rough bound.
First, clarify the two methods (e.g., random insertion vs. deterministic spacing) and define what constitutes a 'back-to-back ad' (e.g., two ads in consecutive posts). Then, for each method, model the sequence of 100 posts as a series of Bernoulli trials or a Markov chain, and compute the probability of at least one occurrence of two consecutive ads using complementary counting or dynamic programming.
Pro tip: Always state your assumptions explicitly (e.g., independence, ad probability) and mention that in real-world settings, ad placement is often not independent, so you would validate with simulation or historical data. This shows you understand the gap between theoretical models and production systems.
Ask or state what the two methods are (e.g., independent random placement with probability p vs. fixed spacing) and define 'back-to-back ads' as two ads in consecutive posts. Confirm the total number of posts (100) and whether ads can appear in the first or last post.
For the random method, assume each post is an ad independently with probability p. For the deterministic method, specify the pattern (e.g., every k-th post is an ad). Write down the probability model for each.
Use complementary counting: P(at least one pair) = 1 - P(no two consecutive ads). For the random method, derive or recall the formula for no consecutive successes in n trials. For the deterministic method, check if the pattern inherently creates back-to-back ads.
Substitute n=100 and the given p (or k) into the formulas. Calculate the numerical probabilities for each method and compare them to see which method yields a higher chance of back-to-back ads.
Mention that you would verify the analytical result with a quick Monte Carlo simulation, especially if the model is complex. Also consider edge cases like p=0, p=1, or k=1.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Users probably prefer Method B because it's more predictable and avoids the jarring experience of seeing a cluster of ads.
First clarify the two methods being compared and define the evaluation criteria for both user and platform perspectives. Then systematically compare the methods across those criteria, highlighting trade-offs and aligning your recommendation with Meta's business goals and user value.
Pro tip: Acknowledge that the 'best' method often depends on context—such as user segment, product maturity, or short-term vs. long-term goals—and propose a hybrid or phased approach when appropriate.
Restate the two methods in your own words and ask clarifying questions about the product, user base, and success metrics if needed.
List criteria for user perspective (e.g., usability, satisfaction, trust) and platform perspective (e.g., engagement, revenue, scalability, cost).
Analyze each method's strengths and weaknesses for both perspectives, using data or examples to support your points.
Weigh the trade-offs and give a clear recommendation, explaining how it balances user and platform needs and aligns with Meta's goals.
Discuss any downsides of your recommendation and how you would monitor or mitigate them, showing forward-thinking.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the two ad insertion methods and the goal of the experiment (e.g., maximize revenue, user experience, or both). Then outline a randomized controlled experiment (A/B test) with proper randomization, metrics, and statistical analysis plan, while addressing practical constraints like network effects and long-term effects.
Pro tip: Emphasize the importance of defining a clear primary metric and guardrail metrics upfront, and discuss how you would handle potential interference between users (e.g., via cluster randomization) to avoid biased results.
Clearly state the null and alternative hypotheses, and select primary, secondary, and guardrail metrics (e.g., ad revenue, user engagement, ad load, user satisfaction).
Choose randomization unit (user, session, or cluster), determine sample size and power, and decide on control/treatment groups. Consider blocking or stratification if needed.
Identify potential sources of bias (e.g., network effects, novelty effects) and design mitigation strategies (e.g., cluster randomization, holdout groups, long-run measurement).
Run the experiment, monitor for data quality issues, and ensure no unintended interference. Use sequential testing or fixed horizon based on trade-offs.
Perform statistical analysis (e.g., t-test, CUPED, bootstrapping) to compare metrics, check for heterogeneity, and make a data-driven recommendation considering business impact.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.