5923概率简单数值题medium

Full-Information Uniform Stopping

题目

You observe up to three independent draws from the Uniform(0,1) distribution, one at a time, and after each you may stop and collect the value just seen or discard it and continue (no recall of discarded values). If you reach the third draw you must take it. Knowing the distribution exactly, what stopping policy maximizes the expected value collected, and what is that expected value?

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