Robbins' Problem (of Optimal Stopping)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, Robbins'' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. Its statement is as follows. Let X1, ... , Xn be independent, identically distributed random variables, uniform on [0, 1]. We observe the Xk''s sequentially and must stop on exactly one of them. No recall of preceding observations is permitted. What stop...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, Robbins'' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. Its statement is as follows. Let X1, ... , Xn be independent, identically distributed random variables, uniform on [0, 1]. We observe the Xk''s sequentially and must stop on exactly one of them. No recall of preceding observations is permitted. What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value?
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