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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> 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}</...") |
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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 [[guide:1cf65e65b3#thm 3.3 |(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. | |||
fair coin exactly <math>n</math> heads turn up. Using Stirling's formula [[guide:1cf65e65b3#thm 3.3 |(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. | |||
Latest revision as of 00:03, 13 June 2024
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.