Binomial distribution: the Galton board

<p class="paragraph-header">Binomial formulae</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 480px;"><colgroup><col style="width: 25.0000%;"><col style="width: 25.0000%;"><col style="width: 25.0000%;"><col style="width: 25.0000%;"></colgroup><thead><tr style="height: 38px;"><th style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">Distribution of $X$</th><th style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">$\mathrm{P}(X = x)$</th><th style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">Mean</th><th style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">Variance</th></tr></thead><tbody><tr style="height: 38px;"><td style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center"><p>Binomial $\mathrm{B} (n, p)$</p></td><td style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">$\binom{n}{x} p^x (1 - p)^{n-x}$</td><td style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">$np$</td><td style="height: 38px; min-height: 38px; text-align: center; --cell-justify: center">$np(1 - p)$</td></tr></tbody></table></div></div>
<p class="paragraph-header">Calculator</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 350px;"><colgroup><col style="width: 42.8571%;"><col style="width: 57.1429%;"></colgroup><thead><tr style="height: 33px;"><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>Probability mass function (calculator binompdf)</p></th><th style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$\mathrm{P}\left( X=x \right)$</p></th></tr></thead><tbody><tr style="height: 33px;"><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>Cumulative distribution function (calculator binomcdf)</p></td><td style="height: 33px; min-height: 33px; text-align: center; --cell-justify: center"><p>$\mathrm{P}\left( X\le a \right)=\mathrm{P}\left( 0\le X\le a \right)$</p></td></tr></tbody></table></div></div>

<p>Probability mass function (calculator binompdf)</p>

<p>Cumulative distribution function (calculator binomcdf)</p>

<p>$\mathrm{P}\left( X\le a \right)=\mathrm{P}\left( 0\le X\le a \right)$</p>

Discrete Random Variables (DRV) - Binomial Probabilities Using Technology

Discrete Random Variables (DRV) - Binomial Probabilities Using Technology

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