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Meta·Data Scientist·Technical Phone Screen·Senior

Senior
Jun 2026

Summary

Meta data scientist interview with a deep stats question about modeling user behavior distributions. Single question but it had four layered parts and felt more like a take-home problem squeezed into a live session. Pretty intense for what I expected.

Questions Asked (1)

Q1

You have a new user cohort. Model the distribution of P2P transfer counts per user in the first 30 days after signup: justify your choice of distributional family including zero-mass and heavy-tail behavior, sketch where mode, median, mean, and 95th percentile fall relative to each other and why, predict how the distribution shifts by day 60 given retention effects and fraud suppression, and recommend two executive-level summary statistics robust to heavy tails plus one diagnostic to validate your assumptions.

Product Analytics & MetricsData ModelingA/B Testing & Experimentation
Author's notes

Four sub-questions in one.

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AI HintsAI Generated

Suggested Approach

Start by framing the problem as modeling a count distribution with excess zeros and a heavy right tail, then justify a zero-inflated negative binomial or hurdle model. Sketch the relative positions of the mode, median, mean, and 95th percentile, and explain how retention and fraud suppression shift the distribution by day 60. Finally, recommend robust executive metrics (e.g., median and 90th percentile) and a diagnostic like a zero-inflation test or QQ plot.

Pro tip: Emphasize that heavy tails make the mean misleading; executives should focus on percentiles and the proportion of users with zero transfers. Also, mention that fraud suppression may truncate the tail, so monitor both the tail and the zero mass over time.

1. Choose distributional family

Justify a zero-inflated negative binomial (ZINB) or hurdle model because transfer counts are overdispersed, have excess zeros (many users never transfer), and a heavy right tail (power users).

2. Sketch distribution shape

Explain that the mode is at zero, median is low (e.g., 1-2), mean is pulled right by the tail, and the 95th percentile is much larger (e.g., 10-20). The mean exceeds the median due to right skew.

3. Predict day 60 shifts

Retention effects: surviving users may transfer more, increasing the mean and tail, but fraud suppression may truncate extreme values and increase zeros if fraudulent accounts are removed.

4. Recommend executive metrics

Suggest median transfers per user (robust to outliers) and the 90th percentile (captures heavy users) as summary statistics. Avoid the mean due to heavy tails.

5. Propose diagnostic

Validate assumptions with a zero-inflation test (e.g., Vuong test) or a QQ plot of the fitted distribution against observed counts, and check for overdispersion.

Key Points to Mention

  • Zero-inflation: many users have zero transfers in first 30 days.
  • Heavy tail: a small fraction of users make many transfers, causing overdispersion.
  • Negative binomial vs. Poisson: overdispersion makes Poisson inappropriate.
  • Mean > median > mode due to right skew; 95th percentile far above mean.
  • Retention and fraud suppression can shift both the zero mass and the tail.
  • Robust metrics: median and 90th percentile; diagnostic: zero-inflation test or QQ plot.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.