Optiver Data Scientist Statistics & Math Interview Questions
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Compute probabilities and expectations in random processes
You are asked to solve the following probability/expectation questions. Unless stated otherwise, assume all random choices are uniform and independent...
Solve probability and expectation problems
Probability and Expectation Practice (Take‑home) Assume all coins and dice are fair unless stated otherwise. Show reasoning and final results. 1) Thre...
Compute odds under time pressure
Timed Probability: At Least Two Reds in Three Draws You have an urn with r red, b blue, and g green balls. Let N = r + b + g with r, b, g ≥ 0 and N ≥ ...
Find next terms in sequences
Pattern Recognition: Find the Rule and Next Term You are given 8 number sequences. For each sequence: - Identify a clear rule that generates the terms...
Analyze EV, arbitrage, and bet sizing across games
Betting Games: EV, Variance, Arbitrage, and Sizing Context You will be shown payout tables or odds for three independent games. Your task is to quickl...
Optimize interval-scoring strategy
Five-Round Interval-Estimation Game: Optimal Intervals and Risk Allocation You play five independent rounds. In round i, an unknown numeric answer A i...
Compute expected coin flips to meet on octagon
Meeting Time on a Random Walk Around an Octagon Problem Two independent particles start at opposite vertices (four edges apart) of a regular octagon. ...
Compute expected counters after color elimination
Problem You have a bag with 30 counters: 10 red, 10 yellow, and 10 blue. You draw counters uniformly at random without replacement. Stop the moment th...