Revision as of 03:15, 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> Let <math>b(2n,.5,n)</math> be the probability that in <math>2n</math> tosses of a fair coin exactly <math>n</math> heads turn up. Using Stirling's formula (Theorem), show that <math>b(2n,.5,n) \sim 1/\sqrt{\pi n}</...")
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]
Let [math]b(2n,.5,n)[/math] be the probability that in [math]2n[/math] tosses of a
fair coin exactly [math]n[/math] heads turn up. Using Stirling's formula (Theorem), show that [math]b(2n,.5,n) \sim 1/\sqrt{\pi n}[/math]. Use the program BinomialProbabilities to compare this with the exact value for [math]n = 10[/math] to 25.