Estimation & Analytical Thinking Questions
Estimation techniques (e.g., Fermi problems, back-of-the-envelope calculations) and analytical problem-solving approaches used in technical interviews and software engineering. Covers problem decomposition, quantitative reasoning, data interpretation, and constructing defensible assumptions to reach plausible conclusions.
HardTechnical
0 practiced
You run 100 metrics in an A/B test and find 5 metrics statistically significant at p < 0.05. Explain why this might be misleading, describe multiple-comparison corrections (e.g., Bonferroni, Benjamini-Hochberg), and propose a practical approach a PM should use to balance discovery vs false positives in product experiments.
MediumTechnical
0 practiced
Explain regression to the mean and provide a product example where it might lead to incorrect conclusions about a feature or experiment (e.g., acting on an unusually high-performing cohort). Describe concrete strategies a PM should use to avoid being misled.
MediumSystem Design
0 practiced
Design a back-of-the-envelope estimate for peak requests per second (RPS) for a new messaging feature given 10M monthly active users. Assume average 30 sessions/month per active, 10 requests per session, and 95th-percentile concurrency of 0.5% of active users. State all assumptions, compute peak RPS, and outline how you'd validate with telemetry.
HardTechnical
0 practiced
Forecast monthly revenue for the next 12 months for a retail product with strong seasonality and planned promotional campaigns. Describe a modeling approach that incorporates historical seasonality, promotion lift (as event regressors), trend, and uncertainty. Explain additive vs multiplicative effects, validation approach, and how you'd present confidence bands to stakeholders.
HardTechnical
0 practiced
Choose between funding Feature X (expected EV $5M, 60% confidence, 12-month time-to-market) and Market Y expansion (expected EV $3.5M, 90% confidence, 6-month time-to-market, $1M initial investment). Estimate NPV over 2 years with a discount rate of 10%, show calculations, and recommend which to fund, including qualitative strategic considerations.
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