Estimate free-trial conversion probability
Overview
This question evaluates a data scientist's competency in cohort definition, censored-data handling, segmentation and confounding assessment, and uncertainty quantification for measuring free-trial to paid conversion, and it belongs to the Analytics & Experimentation domain within data science.
IBM
Jan 17, 2026, 12:00 AM
Data Scientist
Technical Screen
Analytics & Experimentation
0
0
Context
A product offers a free trial. You are asked: “What is the probability of conversion for a group of people who started a free trial?”
Data (assume available)
A table of trial starts:
-
user_id -
trial_start_at(timestamp) -
trial_length_days(int) -
country/channel/plan/device(optional segments)
A table of paid conversions:
-
user_id -
paid_start_at(timestamp, nullable if never converted) -
revenue(optional)
Task
- Define precisely what “conversion probability” means, including the time window and cohort definition.
-
Show how you would estimate the conversion probability for a cohort of trial starters, including how you would handle:
- users whose trial has not ended yet (incomplete observation)
- delayed conversions (convert after trial)
- segmentation and potential confounding (e.g., channel mix changes)
- Provide a way to quantify uncertainty (confidence/credible intervals) and communicate results.
- Suggest follow-up analyses/metrics (diagnostics and guardrails) to ensure the estimate is decision-useful.
Solution
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