exercise:44e18f4b7e: 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> Suppose that in the hypergeometric distribution, we let <math>N</math> and <math>k</math> tend to <math>\infty</math> in such a way that the ratio <math>k/N</math> approaches a real number <math>p</math> between 0 and 1. Show that the hypergeome...") |
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Suppose that in the hypergeometric distribution, we let <math>N</math> and <math>k</math> tend to <math>\infty</math> in such a way that the ratio <math>k/N</math> approaches a real number <math>p</math> between 0 and 1. Show that the hypergeometric distribution tends to | |||
<math>N</math> and <math>k</math> tend to <math>\infty</math> in such a way that the ratio <math>k/N</math> approaches | |||
a real number <math>p</math> between 0 and 1. Show that the hypergeometric distribution tends to | |||
the binomial distribution with parameters <math>n</math> and <math>p</math>. | the binomial distribution with parameters <math>n</math> and <math>p</math>. | ||
Latest revision as of 00:23, 14 June 2024
Suppose that in the hypergeometric distribution, we let [math]N[/math] and [math]k[/math] tend to [math]\infty[/math] in such a way that the ratio [math]k/N[/math] approaches a real number [math]p[/math] between 0 and 1. Show that the hypergeometric distribution tends to the binomial distribution with parameters [math]n[/math] and [math]p[/math].