5935概率中等数值题medium
Hiring With an Interview Cost
题目
Three candidates of distinct unknown qualities arrive in uniformly random order; each candidate must be interviewed (in order) before you can judge their relative rank, and conducting each interview costs 0.05 utility. After interviewing a candidate you immediately and irrevocably hire or reject (if you reach the third you must hire). You receive payoff 1 if you hire the overall best candidate and 0 otherwise, minus the total interview cost incurred. Among the threshold rules 'reject the first r interviewed, then hire the first later record', find the optimal r and the resulting expected net payoff.
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