world:enigmahanoi
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world:enigmahanoi [2020/04/20 11:28] rdouc |
world:enigmahanoi [2022/04/28 14:22] rdouc [A first illustrative example] |
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| - | <note warning>Two different real numbers are in a basket but we don't have access to their values. Pick at random one of them in the basket with equal probabilities and see its value. The question is to find a decision process which allows you to indicate, with a probability strictly larger than $1/2$, which one is the largest . </note> | + | <note tip>Two different real numbers are in a basket but we don't have access to their values. Pick at random one of them in the basket with equal probabilities and see its value. The question is to find a decision process which allows you to indicate, with a probability strictly larger than $1/2$, which one is the largest . </note> |
| <hidden Answer> $ \newcommand{\rset}{\mathbb R} \newcommand{\PP}{\mathbb P}$ Denote by $X$ the chosen real number that you have in your hand. Let $\alpha: \rset \to (0,1)$ be a (strictly) increasing measurable function. With a probability $\alpha(X)$, say that the largest real number is the one in your hand and otherwise say that this is the one in the basket. | <hidden Answer> $ \newcommand{\rset}{\mathbb R} \newcommand{\PP}{\mathbb P}$ Denote by $X$ the chosen real number that you have in your hand. Let $\alpha: \rset \to (0,1)$ be a (strictly) increasing measurable function. With a probability $\alpha(X)$, say that the largest real number is the one in your hand and otherwise say that this is the one in the basket. | ||
world/enigmahanoi.txt · Last modified: 2022/04/28 14:27 by rdouc
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