exercise:Ff564a4e19: 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> Choose a number <math>B</math> ''at random'' from the interval <math>[0,1]</math> with uniform density. Find the probability that <ul><li> <math>1/3 < B < 2/3</math>. </li> <li> <math>|B - 1/2| \leq 1/4</math>. </li> <li> <math>B < 1/4</mat...") |
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\newcommand{\mathds}{\mathbb}</math></div> Choose a number <math>B</math> ''at random'' from the | \newcommand{\mathds}{\mathbb}</math></div> Choose a number <math>B</math> ''at random'' from the | ||
interval <math>[0,1]</math> with uniform density. Find the probability that | interval <math>[0,1]</math> with uniform density. Find the probability that | ||
<ul><li> <math>1/3 < B < 2/3</math>. | <ul style="list-style-type:lower-alpha"><li> <math>1/3 < B < 2/3</math>. | ||
</li> | </li> | ||
<li> <math>|B - 1/2| \leq 1/4</math>. | <li> <math>|B - 1/2| \leq 1/4</math>. | ||
Latest revision as of 22:38, 12 June 2024
[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]
Choose a number [math]B[/math] at random from the
interval [math][0,1][/math] with uniform density. Find the probability that
- [math]1/3 \lt B \lt 2/3[/math].
- [math]|B - 1/2| \leq 1/4[/math].
- [math]B \lt 1/4[/math] or [math]1 - B \lt 1/4[/math].
- [math]3B^2 \lt B[/math].