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Hard · Conditional Expected Value · Quant Trader interview question · optimal-stopping, secretary-problem, probability, expected-value, mental-math
You are interviewing $N$ candidates for a single position. You can only hire one candidate, and once rejected, a candidate cannot be recalled. You observe each candidate's performance and must immediately decide whether to hire them. Your goal is to maximize the probability of hiring the best candidate. Instead of using the standard $1/e$ stopping rule, you decide to split the candidates into two groups. You observe the first $m$ candidates, record the best candidate in that group, and then hire