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