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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> Four women, A, B, C, and D, check their hats, and the hats are returned in a random manner. Let <math>\Omega</math> be the set of all possible permutations of A, B, C, D. Let <math>X_j = 1</math> if the <math>j</math>th woman gets her own hat ba...") |
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Four women, A, B, C, and D, check their hats, and the hats are returned in a random manner. Let <math>\Omega</math> be the set of all possible permutations of A, B, C, D. Let <math>X_j = 1</math> if the <math>j</math>th woman gets her own hat back and 0 otherwise. What is the | |||
in a random manner. Let <math>\Omega</math> be the set of all possible permutations of A, B, C, D. Let | |||
<math>X_j = 1</math> if the <math>j</math>th woman gets her own hat back and 0 otherwise. What is the | |||
distribution of <math>X_j</math>? Are the <math>X_i</math>'s mutually independent? | distribution of <math>X_j</math>? Are the <math>X_i</math>'s mutually independent? | ||
Latest revision as of 01:04, 13 June 2024
Four women, A, B, C, and D, check their hats, and the hats are returned in a random manner. Let [math]\Omega[/math] be the set of all possible permutations of A, B, C, D. Let [math]X_j = 1[/math] if the [math]j[/math]th woman gets her own hat back and 0 otherwise. What is the distribution of [math]X_j[/math]? Are the [math]X_i[/math]'s mutually independent?