Calculate conditional probability for user retention
Last updated: August 7, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Twilio
August 7, 202556
3
4,524 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Twilio asks this during the Technical Screen to assess your experimentation skills. They want to see how you define success metrics, design controlled experiments, and interpret results with appropriate statistical rigor.
What the Interviewer Expects
- Define clear success metrics aligned with business goals
- Propose a basic experimental design with control and treatment groups
- Interpret results correctly and draw reasonable conclusions
- Identify obvious confounding variables
Key Topics to Cover
How to Approach This
- Define success metrics carefully. A good metric is measurable, actionable, and aligned with business goals.
- Run experiments long enough to account for novelty effects and weekly seasonality.
- Use funnel analysis to identify where users drop off for maximum optimization impact.
- Segment results by key dimensions (platform, country, user cohort) to catch hidden patterns.
- Consider network effects and interference between treatment and control groups.
Possible Follow-up Questions
- How would you handle seasonality in your experiment?
- What if the experiment shows a positive short-term effect but you suspect a negative long-term impact?
- How would you handle interference between treatment and control?
- What if you discover a bug in the logging during the experiment?
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Browse Analytics QuestionsSample Answer
Problem Setup
To calculate the conditional probability for user retention at Twilio, we need to define our analytical question clearly: "What is the probability that a user who generates high revenue per session wi...
Methodology
For this analysis, we will employ a conditional probability approach combined with a chi-square test to evaluate the association between revenue per session and user retention. Specifically, we will c...
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