exercise:8765f28a00: 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> Suppose you choose two numbers <math>x</math> and <math>y</math>, independently at random from the interval <math>[0,1]</math>. Given that their sum lies in the interval <math>[0,1]</math>, find the probability that <ul><li> <math>|x - y| < 1</...") |
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Suppose you choose two numbers <math>x</math> and <math>y</math>, independently at random from the interval <math>[0,1]</math>. Given that their sum lies in the interval <math>[0,1]</math>, | |||
the interval <math>[0,1]</math>. Given that their sum lies in the interval <math>[0,1]</math>, | |||
find the probability that | find the probability that | ||
<ul><li> <math>|x - y| < 1</math>. | |||
<ul style="list-style-type:lower-alpha"><li> <math>|x - y| < 1</math>. | |||
</li> | </li> | ||
<li> <math>xy < 1/2</math>. | <li> <math>xy < 1/2</math>. | ||
Latest revision as of 00:34, 14 June 2024
Suppose you choose two numbers [math]x[/math] and [math]y[/math], independently at random from the interval [math][0,1][/math]. Given that their sum lies in the interval [math][0,1][/math], find the probability that
- [math]|x - y| \lt 1[/math].
- [math]xy \lt 1/2[/math].
- [math]\max\{x,y\} \lt 1/2[/math].
- [math]x^2 + y^2 \lt 1/4[/math].
- [math]x \gt y[/math].