exercise:289ed5c286: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Let <math>n</math> be a positive integer. Let <math>S</math> be the set of integers between 1 and <math>n</math>. Consider the following process: We remove a number from <math>S</math> at random and write it down. We repeat this until <math>S<...") |
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Let <math>n</math> be a positive integer. Let <math>S</math> be the set of integers between 1 and | |||
integers between 1 and | |||
<math>n</math>. Consider the following process: We remove a number from <math>S</math> at random and write it down. | <math>n</math>. Consider the following process: We remove a number from <math>S</math> at random and write it down. | ||
We repeat this until <math>S</math> is empty. The result is a permutation of the integers from 1 | We repeat this until <math>S</math> is empty. The result is a permutation of the integers from 1 | ||
to <math>n</math>. Let <math>X</math> denote this permutation. Is <math>X</math> uniformly distributed? | to <math>n</math>. Let <math>X</math> denote this permutation. Is <math>X</math> uniformly distributed? | ||
Latest revision as of 00:59, 14 June 2024
Let [math]n[/math] be a positive integer. Let [math]S[/math] be the set of integers between 1 and [math]n[/math]. Consider the following process: We remove a number from [math]S[/math] at random and write it down. We repeat this until [math]S[/math] is empty. The result is a permutation of the integers from 1 to [math]n[/math]. Let [math]X[/math] denote this permutation. Is [math]X[/math] uniformly distributed?