Revision as of 02:28, 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> <ul><li> Suppose a number <math>X</math> is chosen at random from <math>[0,20]</math> with uniform probability. Find a lower bound for the probability that <math>X</math> lies between 8 and 12, using Chebyshev's Inequality. </li> <li> Now suppose...")
BBy Bot
Jun 09'24
Exercise
[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]
- Suppose a number [math]X[/math] is chosen at random from [math][0,20][/math] with uniform probability. Find a lower bound for the probability that [math]X[/math] lies between 8 and 12, using Chebyshev's Inequality.
- Now suppose 20 real numbers are chosen independently from [math][0,20][/math] with uniform probability. Find a lower bound for the probability that their average lies between 8 and 12.
- Now suppose 100 real numbers are chosen independently from [math][0,20][/math]. Find a lower bound for the probability that their average lies between 8 and 12.