Upstart Data Scientist Statistics & Math Interview Questions
Practice 15 real Statistics & Math interview questions for Data Scientist roles at Upstart.

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Correct length-biased sampling from family-size survey
In a town, you visit a school and ask 100 kids: “How many children are in your family?” You observe: - 50 kids say their family has 1 child - 20 kids ...
Compute decay, OLS, and classic probability results
You are asked several probability/statistics questions. 1) Radioactive decay (half-life) A radioactive atom has a half-life of 1 day. Assume each atom...
Solve core probability/statistics mini-problems
Answer the following probability/statistics interview questions. Assume all randomness is independent unless stated otherwise. 1) Radioactive decay (h...
Solve drunk-passenger probability and simulate outcome
Lost Boarding Pass Puzzle: Last Passenger's Seat Context: Technical screen for a Data Scientist (Statistics & Math). Setup - There are n passengers la...
Combine noisy thermometers; compute random-walk correlations
Problem 1: Estimating a true temperature from noisy thermometers Assume the true (fixed) temperature is an unknown constant \(\theta\). 1a) One thermo...
Calculate Expected Streaks in Coin Toss Sequence
Expected Number of Streaks in Coin Tosses Scenario You toss a coin repeatedly. A "streak" (a run) begins on the first toss and whenever the current to...
Analyze HT vs HH stopping-time probabilities
Coin-Flip Stopping Game: HT vs HH You repeatedly flip a coin until either the pattern HT appears (Player A wins) or the pattern HH appears (Player B w...
Interpret A/B results with p-values and uncertainty
A/B Test: Effect Sizes, CIs, Multiple Testing, Power, and Decision Context: You ran a 14‑day experiment (2025‑08‑15 → 2025‑08‑28) with 1:1 allocation ...
Determine distribution of aX+b when X~N(0,1)
Linear Transform of a Standard Normal Setup - Let X ~ N(0, 1) (standard normal). - For constants a, b ∈ ℝ, define Y = aX + b. Tasks (a) What is the ex...
Calculate Particle Survival Probability After Time t
Radioactive-Decay Style Probability Context You have 100 identical, independent particles. Each particle's lifetime is exponentially distributed with ...
Identify binomial model and compute moments
Tossing N Balls Into a Cup (Independent Hits with Probability p) You toss N independent balls toward a cup. Each ball lands in the cup with probabilit...
Assess Probability of Heads in Coin Tosses
Probability with Coin Tosses and the Normal Distribution Context Onsite data scientist screening question assessing basic probability and distribution...
Estimate and Derive Regression Coefficient for X on y
Statistics & Probability Onsite — Two-Part Question Context - You have a simple linear data-generating process: y = X + ε, where X and ε are independe...
Estimate one-child household probability
You survey 100 children at a school and ask how many children are in their family. The responses are: - 50 children say their family has 1 child - 20 ...
Estimate Family Proportions and Explain Regression Anomalies
On-site Statistics Round Task Overview You are given a population of families that have either 1, 2, or 3 children. You sample 100 children (i.e., the...