Analyze Distribution of Daily Page Shares Per User

Quick Overview

Meta statistics prompt on daily page-share and time-spent distributions, covering zero inflation, heavy tails, percentiles, cohort regression, negative-binomial-style models, variance, and tail stability.

Analyze Distribution of Daily Page Shares Per User

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Onsite

##### Question Sketch the distribution of daily page shares per user, indicating mean, median, p1, and p99. What shape do you expect and why? For users at the 50th and 95th percentiles of today’s distribution, predict their average shares two weeks from now. For the cohort with exactly two shares on day 1, describe the expected trend of average shares over days 2–30. Repeat for the cohort with five shares; which cohort will have larger variance and what distribution do you expect? Repeat the above style of analysis for daily time-spent-per-user; comment on stability of mean and tail behavior over three weeks. ##### Hints Engagement metrics are typically heavy-tailed; cohorts regress toward the overall mean while retaining right-skewed structure.

Quick Answer: Meta statistics prompt on daily page-share and time-spent distributions, covering zero inflation, heavy tails, percentiles, cohort regression, negative-binomial-style models, variance, and tail stability.

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Jul 12, 2025, 6:59 PM
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Engagement Distributions and Cohort Dynamics

You are analyzing per-user, per-day engagement. Assume the panel includes all users, inactive days count as zeros, and bots or obvious spam accounts have been removed.

Constraints & Assumptions

  • Daily page shares are count data and are likely zero-inflated, overdispersed, and right-skewed.
  • Users have heterogeneous long-run sharing propensities and day-to-day randomness.
  • Percentile-selected cohorts can regress toward the population mean over time.
  • Daily time spent is nonnegative, heavy-tailed, and may be censored or capped by measurement rules.

Clarifying Questions to Ask Guidance

  • Are inactive users included as zero-share days?
  • Are we analyzing users, active users, or sessions?
  • Is the goal descriptive reporting, forecasting, or anomaly detection?
  • Are shares and time spent measured consistently across platforms and time zones?

What a Strong Answer Covers Guidance

  • Distribution sketch for daily shares: a spike at zero, long right tail, mean greater than median, p1 often zero, and p99 far to the right.
  • Explanation of zero inflation, heavy tails, heterogeneous user propensities, burstiness, and event-driven behavior.
  • Prediction for users at today's 50th and 95th percentiles: both should be estimated from historical transition/cohort data, with high-percentile users regressing downward while remaining above average.
  • Cohort trajectories for exactly 2 and exactly 5 shares on day 1, including regression toward each cohort's latent mean and wider variance for the higher-activity cohort.
  • Suitable count distributions or models, such as zero-inflated negative binomial, Poisson-gamma mixtures, hurdle models, or user-level random effects.
  • Similar analysis for time spent, including heavy tail, stability of mean versus tail percentiles, winsorization/capping, and cohort persistence over three weeks.

Follow-up Questions Guidance

  • Why can the mean be unstable for heavy-tailed engagement metrics?
  • How would you estimate the two-week forecast empirically?
  • What would you do if p99 jumps but the median is unchanged?
  • How would bot filtering change the distribution?
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