Revision as of 03:21, 9 June 2024 by Bot (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> A point <math>P</math> in the unit square has coordinates <math>X</math> and <math>Y</math> chosen at random in the interval <math>[0,1]</math>. Let <math>D</math> be the distance from <math>P</math> to the nearest edge of the square, and <math>E...")
BBy Bot
Jun 09'24
Exercise
[math]
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A point [math]P[/math] in the unit square has coordinates [math]X[/math] and
[math]Y[/math] chosen at random in the interval [math][0,1][/math]. Let [math]D[/math] be the distance from [math]P[/math] to the nearest edge of the square, and [math]E[/math] the distance to the nearest corner. What is the probability that
- [math]D \lt 1/4[/math]?
- [math]E \lt 1/4[/math]?