Upstart Data Scientist Statistics & Math Interview Questions
Practice the exact questions companies are asking right now.

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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 ...
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...
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...
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...
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...
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 ...
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 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 ...
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...
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...
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...
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...
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 ...
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...