exercise:859017a64b: 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> In the hat check problem (see Example), it was assumed that <math>N</math> people check their hats and the hats are handed back at random. Let <math>X_j = 1</math> if the <math>j</math>th person gets his or her hat...") |
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In the hat check problem (see [[guide:E54e650503#exam 3.13 |Example]]), it was assumed that <math>N</math> people check their hats and the hats are handed back at random. Let <math>X_j = 1</math> if the <math>j</math>th person gets his or her hat and 0 | |||
was assumed that <math>N</math> people check their hats and the hats are handed | |||
back at random. Let <math>X_j = 1</math> if the <math>j</math>th person gets his or her hat and 0 | |||
otherwise. Find <math>E(X_j)</math> and <math>E(X_j \cdot X_k)</math> for <math>j</math> not equal to <math>k</math>. Are <math>X_j</math> | otherwise. Find <math>E(X_j)</math> and <math>E(X_j \cdot X_k)</math> for <math>j</math> not equal to <math>k</math>. Are <math>X_j</math> | ||
and <math>X_k</math> independent? | and <math>X_k</math> independent? | ||
Latest revision as of 16:31, 14 June 2024
In the hat check problem (see Example), it was assumed that [math]N[/math] people check their hats and the hats are handed back at random. Let [math]X_j = 1[/math] if the [math]j[/math]th person gets his or her hat and 0 otherwise. Find [math]E(X_j)[/math] and [math]E(X_j \cdot X_k)[/math] for [math]j[/math] not equal to [math]k[/math]. Are [math]X_j[/math] and [math]X_k[/math] independent?