Characterize and compare transfer-count distributions over time

For a fresh cohort, define $X$ as the count of peer-to-peer transfers a user makes within the first 30 days after signing up. 1) Make a case for a reasonable distribution family for $X$ (such as a zero-inflated negative binomial or a lognormal mixture), and explain why we should expect a large zero mass and a heavy right tail. 2) Outline the probable order and rough positions of the mode, median, mean, and 95th percentile for $X$, and explain why these summaries are not the same. 3) Describe how the distribution should change by day 60, considering retention-based selection, habit formation, fraud suppression, and seasonality, and predict the direction in which those four summaries move. 4) Suggest two robust executive-facing summary statistics that hold up under heavy tails (for example, a trimmed mean or a median of ratios), plus one diagnostic (such as a QQ plot or a tail index) for checking the assumptions.

The question tests whether a candidate can model zero-inflated, heavy-tailed count data, interpret distribution summaries and percentiles, reason through time-based shifts driven by retention and fraud dynamics, and choose robust summary statistics and diagnostics for a Data Scientist position.

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