Capital One Data Scientist Statistics & Math Interview Questions
Practice 57 real Statistics & Math interview questions for Data Scientist roles at Capital One.
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Derive E[X^2] from mgf e^{t^2}
Identify Distribution and Compute E[X^2] from an MGF You are given a random variable X with moment-generating function (mgf): - M_X(t) = E[e^{tX}] = e...
Diagnose and fix a flight-delay modeling setup
Flight Delay Modeling: Binary Target, Features, and Diagnostics You are modeling the probability that a flight arrives with a delay greater than 15 mi...
Compute Optimal Die Re-roll Strategy
This question evaluates a candidate's understanding of optimal stopping, expected-value computation, and decision-making under uncertainty in probabil...
Compute Groupon unit economics and break-even
Restaurant Coupons and Unit Economics Context: A restaurant's variable cost (VC) is 40% of pre-discount spend and fixed cost (FC) is $100/day. Assume ...
Compute optimal stopping in a die-rolling game
Optimal stopping with a fair die (3-roll horizon) You observe outcomes of fair six-sided die rolls (faces 1–6) and may stop after any roll to take the...
Determine Claim Rate for Breakeven in Insurance Portfolio
Weather-Insurance Portfolio Profitability You price a 12-month weather insurance policy. Customers pay premiums upfront for the year. Each policy can ...
How to Analyze and Reduce Airline Flight Delays
How to Analyze and Reduce Airline Flight Delays Scenario Statistics role-play: investigating airline flight delays Task Design and execute a statistic...
How do you compute expected return for two projects?
This question evaluates a candidate's ability to compute expected return and net present value by modeling probabilistic outcomes, cash flows, discoun...
Compute credit-card portfolio profit and breakeven
A bank is evaluating a new credit card. Segments: A: 30,000 customers, capture rate 20%, avg annual spend per captured customer = $100,000. B: any pop...
Compute and interpret 95% confidence intervals
Answer all parts. Show formulas and intermediate values. A) An A/B test measures conversion: Variant A has 410 conversions out of 5000 visitors; Varia...
Match Netflix profit; derive required subscribers
Subscription Profit and Break-even (All Monthly) Assume all figures are monthly and "M" denotes millions. We model subscription profit as: - Profit = ...
Compute profit and surge break‑even price
Capacity and Break-even Pricing for a Ride-share Service Context: You manage daily capacity and pricing for a ride‑share service. Each driver works an...
Determine intersection dimension of two 4D subspaces
This question evaluates linear algebra skills—specifically understanding of subspace dimensions, intersections and sums, and the dimension formula for...
Calculate Annual Profit of Credit Card Portfolio
Credit Card Portfolio Annual Profit You manage a portfolio of 500,000 active credit-card accounts. Each active card generates multiple revenue streams...
Set membership fee under investment constraints
Streaming membership pricing vs. content investment Context You are designing a monthly membership for a streaming service. Producing original shows i...
Quantify and Model Flight Delays Using Statistical Tests
Flight Delays: Quantification, Modeling, and Mitigation Testing You are a data scientist investigating flight delays using historical flight records a...
Calculate Incremental Customers for Marketing Spend Justification
Incremental Customers Needed for Marketing Spend You previously computed the per-customer annual profit for a new cardholder, excluding partnership ma...
Compute gala vs online break-even donors
A nonprofit must choose one of two fundraising options. Option A (Gala): capacity 100 attendees; fixed cost $20,000; variable cost $100 per attendee. ...
Compute unit economics and insurance break-even
Subscription unit economics and insurance math. Assume no discounting and ignore taxes unless stated. Part A (15-month term): A subscription service c...
Calculate profit and break-even across pricing models
Unit Economics and Break-even Analysis for a Cloud-Storage Startup You are analyzing a cloud-storage startup that currently charges unit-based pricing...