{"id":233,"date":"2023-08-03T20:59:59","date_gmt":"2023-08-03T20:59:59","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%b4%9f-1-%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T20:59:59","modified_gmt":"2023-08-03T20:59:59","slug":"%e8%b4%9f-1-%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%b4%9f-1-%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83\/","title":{"rendered":"\u8d1f\u4e8c\u9879\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u8d1f\u4e8c\u9879\u5206\u5e03\u53ca\u5176\u7528\u9014\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u516c\u5f0f\u3001\u5177\u4f53\u793a\u4f8b\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u5c5e\u6027\u3002\u6700\u540e\uff0c\u60a8\u5c06\u80fd\u591f\u4f7f\u7528\u5728\u7ebf\u8ba1\u7b97\u5668\u8ba1\u7b97\u4efb\u4f55\u8d1f\u4e8c\u9879\u5206\u5e03\u6982\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-binomial-negativa\"><\/span>\u4ec0\u4e48\u662f\u8d1f\u4e8c\u9879\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u8d1f\u4e8c\u9879\u5206\u5e03<\/strong>\u662f\u4e00\u79cd\u6982\u7387\u5206\u5e03\uff0c\u63cf\u8ff0\u83b7\u5f97\u7ed9\u5b9a\u6570\u91cf\u7684\u6b63\u7ed3\u679c\u6240\u9700\u7684\u4f2f\u52aa\u5229\u8bd5\u9a8c\u6b21\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u5177\u6709\u4e24\u4e2a\u7279\u5f81\u53c2\u6570\uff1a <em>r<\/em>\u662f\u671f\u671b\u7684\u6210\u529f\u7ed3\u679c\u7684\u6570\u91cf\uff0c <em>p<\/em>\u662f\u6267\u884c\u7684\u6bcf\u4e2a\u4f2f\u52aa\u5229\u5b9e\u9a8c\u7684\u6210\u529f\u6982\u7387\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-171122de529a1c006bc46e8d89176016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{BN}(r,p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u4f2f\u52aa\u5229\u6d4b\u8bd5\u662f\u4e00\u79cd\u6709\u4e24\u79cd\u53ef\u80fd\u7ed3\u679c\u7684\u5b9e\u9a8c\uff1a\u201c\u6210\u529f\u201d\u548c\u201c\u5931\u8d25\u201d\u3002\u56e0\u6b64\uff0c\u5982\u679c\u201c\u6210\u529f\u201d\u7684\u6982\u7387\u4e3a<em>p<\/em> \uff0c\u5219\u201c\u5931\u8d25\u201d\u7684\u6982\u7387\u4e3a<em>q=1-p<\/em> \u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8d1f\u4e8c\u9879\u5206\u5e03\u5b9a\u4e49\u4e86\u4e00\u4e2a\u8fc7\u7a0b\uff0c\u5176\u4e2d\u6839\u636e\u9700\u8981\u8fdb\u884c\u5c3d\u53ef\u80fd\u591a\u7684\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4ee5\u83b7\u5f97\u6b63<em>\u7ed3\u679c<\/em>\u3002\u6b64\u5916\uff0c\u6240\u6709\u8fd9\u4e9b\u4f2f\u52aa\u5229\u8bd5\u9a8c\u90fd\u662f\u72ec\u7acb\u7684\uff0c\u5e76\u4e14<em>\u6210\u529f<\/em>\u7684\u6982\u7387\u6052\u5b9a\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u670d\u4ece\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u662f\u9ab0\u5b50\u5fc5\u987b\u6eda\u52a8\u7684\u6b21\u6570\uff0c\u76f4\u5230\u6570\u5b57 6 \u6eda\u52a8 3 \u6b21\u4e3a\u6b62\u3002<\/p>\n<p>\u8d1f\u4e8c\u9879\u5206\u5e03\u4e0e\u4e8c\u9879\u5206\u5e03\u7684\u533a\u522b\u5728\u4e8e\uff0c\u8d1f\u4e8c\u9879\u5206\u5e03\u7edf\u8ba1\u7684\u662f\u83b7\u5f97\u4e00\u5b9a\u6570\u91cf\u6210\u529f\u7ed3\u679c\u6240\u9700\u7684\u6b21\u6570\uff0c\u800c\u4e8c\u9879\u5206\u5e03\u7edf\u8ba1\u7684\u662f\u4e00\u7cfb\u5217\u4f2f\u52aa\u5229\u6d4b\u8bd5\u4e2d\u6210\u529f\u6848\u4f8b\u7684\u6570\u91cf\u3002 <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5206\u5e03-1\/\">\u4ec0\u4e48\u662f\u4e8c\u9879\u5206\u5e03\uff1f<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-binomial-negativa\"><\/span>\u8d1f\u4e8c\u9879\u5206\u5e03\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u53c2\u6570<em>r\u3001p\u3001x\uff0c<\/em>\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u6982\u7387\u901a\u8fc7\u5c06<em>xr<\/em>\u4e2d\u7684<em>x-1<\/em>\u7684\u7ec4\u5408\u6570\u4e58\u4ee5<em>(1-p) <sup>xr<\/sup><\/em>\u518d\u4e58\u4ee5<em>p <sup>r<\/sup><\/em>\u6765\u8ba1\u7b97\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u8ba1\u7b97\u8d1f\u4e8c\u9879\u5206\u5e03\u6982\u7387\u7684\u516c\u5f0f<\/strong>\u4e3a\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/formule-de-distribution-binomiale-negative.png\" alt=\"\u8d1f\u4e8c\u9879\u5206\u5e03\u516c\u5f0f\" class=\"wp-image-4813\" width=\"318\" height=\"319\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u53d8\u91cf\u670d\u4ece\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u6982\u7387\u3002<\/u> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-la-distribucion-binomial-negativa\"><\/span>\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u6c42\u89e3\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u5982\u679c\u4f60\u629b\u4e00\u679a\u786c\u5e01\u516b\u6b21\uff0c\u7b2c\u516b\u6b21\u629b\u786c\u5e01\u7b2c\u56db\u6b21\u51fa\u73b0\u6b63\u9762\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u629b\u786c\u5e01\u65f6\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5728\u4e24\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\uff08\u6b63\u9762\u548c\u53cd\u9762\uff09\u4e2d\u53ea\u6709\u4e00\u4e2a\u6b63\u9762\u7ed3\u679c\uff08\u6b63\u9762\uff09\uff0c\u56e0\u6b64\u6210\u529f\u7684\u6982\u7387\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bdceac6409b69d142f23801ec85e2691_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8be5\u95ee\u9898\u4e2d\u7684\u968f\u673a\u53d8\u91cf\u9075\u5faa\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\uff0c\u5176\u4e2d r=4 \u4e14 p=0.5\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u8d1f\u4e8c\u9879\u5206\u5e03\u516c\u5f0f\u6765\u8ba1\u7b97\u7ec3\u4e60\u8981\u6c42\u6211\u4eec\u505a\u7684\u6982\u7387\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bc56100604e5889a6d169c0395f19ebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P[X=x]&amp;=\\begin{pmatrix}x-1\\\\ x-r\\end{pmatrix}\\cdot (1-p)^{x-r}\\cdot p^r\\\\[2ex]\\displaystyle P[X=8]&amp;=\\begin{pmatrix}8-1\\\\ 8-4\\end{pmatrix}\\cdot (1-0,5)^{8-4}\\cdot 0,5^4\\\\[2ex] P[X=8]&amp;=0,1367\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-binomial-negativa\"><\/span>\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4ee5\u4e0b\u662f\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u6700\u91cd\u8981\u7279\u5f81\u3002<\/p>\n<ul>\n<li>\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u7531\u4e24\u4e2a\u7279\u5f81\u53c2\u6570\u5b9a\u4e49\uff1a <em>r<\/em>\u662f\u671f\u671b\u7684\u6210\u529f\u7ed3\u679c\u7684\u6570\u91cf\uff0c <em>p<\/em>\u662f\u6267\u884c\u7684\u6bcf\u4e2a\u4f2f\u52aa\u5229\u5b9e\u9a8c\u7684\u6210\u529f\u6982\u7387\u3002<\/li>\n<\/ul>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{c}r\\in \\mathbb{Z}^+ \\\\[2ex] 0 &lt;ul&gt;&lt;li&gt; The mean of the negative binomial distribution is equal to &lt;em&gt;r&lt;\/em&gt; multiplied by &lt;em&gt;(1-p)&lt;\/em&gt; and divided by &lt;em&gt;p&lt;\/em&gt; . Thus the formula which makes it possible to calculate the mean of a negative binomial distribution is the following: &lt;\/li&gt;&lt;\/ul&gt;[latex]E[X]=\\cfrac{r\\cdot (1-p)}{p}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{c}\nPlease use \\mathaccent for accents in math mode.\nleading text: ...The mean of the binomial distribution born\nPlease use \\mathaccent for accents in math mode.\nleading text: ... the negative binomial distribution is\nPlease use \\mathaccent for accents in math mode.\nleading text: ...negative binomial distribution is equal to\nPlease use \\mathaccent for accents in math mode.\nleading text: ...gative is equal to &lt;em&gt;r&lt;\/em&gt; multiplied\nPlease use \\mathaccent for accents in math mode.\nleading text: ...m&gt; multiplied by &lt;em&gt;(1-p)&lt;\/em&gt; and divided\nPlease use \\mathaccent for accents in math mode.\nleading text: ...the mean of a binomial distribution born\n\\begin{array} on input line 8 ended by \\end{document}.\n\n<\/pre>\n<ul>\n<li>\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u65b9\u5dee\u7b49\u4e8e<em>r<\/em>\u4e58\u4ee5<em>(1-p)<\/em>\u9664\u4ee5<em>p <sup>2<\/sup><\/em> \u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c82d66018d0715f20318f383cf7c04c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{r\\cdot (1-p)}{p^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"163\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u53c2\u6570<em>r<\/em>\u5927\u4e8e1\uff0c\u5219\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u4f17\u6570\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-600d3f94b3cd3927f264450bcd043a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lfloor \\frac{(r-1)(1-p)}{p}\\rfloor\\quad \\text{para }r>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;42&#8243; width=&#8221;221&#8243; style=&#8221;vertical-align: -16px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u53ef\u4ee5\u786e\u5b9a\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u6982\u7387\u7684\u8d28\u91cf\u51fd\u6570\u5982\u4e0b\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-beafc8c08e7aad51059349dfd2addd5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X=x]=\\begin{pmatrix}x-1\\\\ x-r\\end{pmatrix}\\cdot (1-p)^{x-r}\\cdot p^r\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"284\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u504f\u5ea6\u7cfb\u6570\u7531\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u8ba1\u7b97\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9bc0a97cdf77d4dd439c71cf8637e53c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{2-p}{\\sqrt{r\\,(1-p)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"122\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li>\u8d1f\u4e8c\u9879\u5206\u5e03\u7684\u5cf0\u5ea6\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-510199601f8ac60aa64008f00d959562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{6}{r} + \\frac{p^2}{r\\,(1-p)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"139\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u53c2\u6570<em>r<\/em>\u7b49\u4e8e 1\uff0c\u5219\u6211\u4eec\u6709<a href=\"https:\/\/statorials.org\/cn\/\u51e0\u4f55\u5206\u5e03\/\">\u51e0\u4f55\u5206\u5e03<\/a>\u7684\u60c5\u51b5\u3002 <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-24bb5ef017a69a1a9de1e07f32412fcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r=1 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad X\\sim \\text{Geometrica}(p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-distribucion-binomial-negativa\"><\/span>\u8d1f\u4e8c\u9879\u5206\u5e03\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c06\u53c2\u6570<em>r\u3001p\u3001x<\/em>\u7684\u503c\u8f93\u5165\u5230\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u4e2d\uff0c\u8ba1\u7b97\u6982\u7387\u3002\u60a8\u5fc5\u987b\u4f7f\u7528\u70b9\u4f5c\u4e3a\u5c0f\u6570\u5206\u9694\u7b26\u8f93\u5165\u6570\u5b57\uff0c\u4f8b\u5982 0.50\u3002<\/p>\n<form action=\"\" method=\"post\">\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span>\u6210\u529f\u7ed3\u679c\u6570\u91cf<span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2060a909f2905bcbe83f8fe9152c2284_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r = \" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span> <input name=\"r\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el valor de r aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span>\u6bcf\u4e2a\u5b9e\u9a8c\u6210\u529f\u7684\u6982\u7387<span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e67f693705a2e492d8981f0ed1387c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p = \" title=\"Rendered by 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