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5939Secretary Selection When Ties Are PossibleThree items arrive in uniformly random order. Their qualities are NOT all distinct: two of them have quality 2 (tied for best) and one has quality 1. After each item you observe its quality relative to those seen so far, reported as 'higher', 'tied', or 'lower' (so a tie is visible). You accept irrevocably or reject (the last is forced). You want to maximize the expected quality of the item you accept. Find the optimal policy and the maximum expected quality, and explain how the possibility of an observed tie changes what you can guarantee.概率中等数值题未尝试免费5940Secretary With an Unknown Number of CandidatesCandidates arrive one at a time in uniformly random order, but the TOTAL number N is itself random: N = 2 with probability 1/2 and N = 3 with probability 1/2, and you do not learn N in advance. After each arriving candidate you observe its rank relative to those seen so far and must irrevocably accept or pass; once the stream ends, if you never accepted you lose. You win only if the candidate you accept is the overall best of all N who arrived. Find the policy that maximizes the win probability and that probability.概率困难数值题未尝试面试订阅