{"id":232,"date":"2023-08-03T21:24:33","date_gmt":"2023-08-03T21:24:33","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%87%a0%e4%bd%95%e5%88%86%e5%b8%831\/"},"modified":"2023-08-03T21:24:33","modified_gmt":"2023-08-03T21:24:33","slug":"%e5%87%a0%e4%bd%95%e5%88%86%e5%b8%831","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%87%a0%e4%bd%95%e5%88%86%e5%b8%831\/","title":{"rendered":"\u51e0\u4f55\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u51e0\u4f55\u5206\u5e03\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u51e0\u4f55\u5206\u5e03\u7684\u5b9a\u4e49\u3001\u51e0\u4f55\u5206\u5e03\u7684\u793a\u4f8b\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u5c5e\u6027\u3002\u6b64\u5916\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u5728\u7ebf\u8ba1\u7b97\u5668\u8ba1\u7b97\u51e0\u4f55\u5206\u5e03\u7684\u4efb\u4f55\u6982\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-geometrica\"><\/span>\u4ec0\u4e48\u662f\u51e0\u4f55\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51e0\u4f55\u5206\u5e03<\/strong>\u662f\u4e00\u79cd\u6982\u7387\u5206\u5e03\uff0c\u5b9a\u4e49\u4e86\u83b7\u5f97\u7b2c\u4e00\u4e2a\u6210\u529f\u7ed3\u679c\u6240\u9700\u7684\u4f2f\u52aa\u5229\u8bd5\u9a8c\u6b21\u6570\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u51e0\u4f55\u5206\u5e03\u6a21\u578b\u662f\u91cd\u590d\u4f2f\u52aa\u5229\u5b9e\u9a8c\u76f4\u5230\u5176\u4e2d\u4e00\u4e2a\u5b9e\u9a8c\u83b7\u5f97\u80af\u5b9a\u7ed3\u679c\u7684\u8fc7\u7a0b\u3002<\/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\u51e0\u4f55\u5206\u5e03\u53d6\u51b3\u4e8e\u53c2\u6570<em>p<\/em> \uff0c\u5b83\u662f\u6240\u6709\u8fdb\u884c\u7684\u5b9e\u9a8c\u6210\u529f\u7684\u6982\u7387\u3002\u6b64\u5916\uff0c\u6240\u6709\u5b9e\u9a8c\u7684\u6982\u7387<em>p<\/em>\u90fd\u662f\u76f8\u540c\u7684\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-22fef9b6ab8e3b351598caf9925c2b3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim\\text{Geom\\'etrica}(p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u540c\u6837\uff0c\u51e0\u4f55\u5206\u5e03\u4e5f\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u7b2c\u4e00\u6b21\u6210\u529f\u4e4b\u524d\u5931\u8d25\u7684\u6b21\u6570\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5206\u5e03\u53ef\u4ee5\u53d6\u503c<em>x=0<\/em> \uff0c\u5e76\u4e14\u5176\u516c\u5f0f\u7565\u6709\u4e0d\u540c\u3002\u4f46\u6700\u5e38\u89c1\u7684\u662f\u56de\u5230\u672c\u8282\u5f00\u5934\u89e3\u91ca\u7684\u51e0\u4f55\u5206\u5e03\u7684\u5b9a\u4e49\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-distribucion-geometrica\"><\/span>\u51e0\u4f55\u5206\u5e03\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u51e0\u4f55\u5206\u5e03\u7684\u5b9a\u4e49\uff0c\u672c\u8282\u5c06\u663e\u793a\u9075\u5faa\u6b64\u7c7b\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u7684\u51e0\u4e2a\u793a\u4f8b\u3002<\/p>\n<p><strong><u style=\"text-decoration-color:#FF8A05\">\u51e0\u4f55\u5206\u5e03\u793a\u4f8b\uff1a<\/u><\/strong><\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u76f4\u5230\u51fa\u73b0\u6b63\u9762\u4e3a\u6b62\u7684\u629b\u786c\u5e01\u6b21\u6570\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5728\u9053\u8def\u4e0a\u7ecf\u8fc7\u76f4\u5230\u770b\u5230\u7ea2\u8272\u6c7d\u8f66\u7684\u6c7d\u8f66\u6570\u91cf\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u4e00\u4e2a\u4eba\u5fc5\u987b\u53c2\u52a0\u9a7e\u9a76\u8003\u8bd5\u76f4\u5230\u901a\u8fc7\u8003\u8bd5\u7684\u6b21\u6570\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u76f4\u5230\u63b7\u51fa\u6570\u5b57 6 \u4e3a\u6b62\u7684\u9ab0\u5b50\u63b7\u6570\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u8fdb\u7403\u524d\u5fc5\u987b\u7f5a\u7403\u7684\u6b21\u6570\u3002<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-geometrica\"><\/span>\u51e0\u4f55\u5206\u5e03\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u51e0\u4f55\u5206\u5e03\u4e2d\uff0c\u5fc5\u987b\u8fdb\u884c<em>x \u6b21<\/em>\u8bd5\u9a8c\u624d\u80fd\u83b7\u5f97\u6b63\u7ed3\u679c\u7684\u6982\u7387\u662f\u53c2\u6570<em>p<\/em>\u4e58\u4ee5<em>(1-p)<\/em><em>\u7684 x-1 \u6b21\u65b9\u7684<\/em>\u4e58\u79ef\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u8ba1\u7b97\u51e0\u4f55\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-geometrique.png\" alt=\"\u51e0\u4f55\u5206\u5e03\u516c\u5f0f\" class=\"wp-image-4723\" width=\"272\" height=\"272\" 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\u9075\u5faa\u51e0\u4f55\u5206\u5e03\u7684\u6982\u7387\u3002<\/u><\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u53ef\u4ee5\u8ba1\u7b97\u51e0\u4f55\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u7684\u5206\u5e03\u51fd\u6570\u516c\u5f0f\u5982\u4e0b\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-88686ff4544e13c6431c27b3fc07076c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X\\leq x]=1-(1-p)^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-la-distribucion-geometrica\"><\/span>\u51e0\u4f55\u5206\u5e03\u7ec3\u4e60\u5df2\u89e3\u51b3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u9ab0\u5b50\u7b2c\u4e09\u6b21\u63b7\u51fa\u6570\u5b57 5 \u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u8be5\u95ee\u9898\u7684\u6982\u7387\u5206\u5e03\u662f\u51e0\u4f55\u5206\u5e03\uff0c\u56e0\u4e3a\u5b83\u5b9a\u4e49\u4e86\u83b7\u5f97\u6210\u529f\u7ed3\u679c\uff08\u6570\u5b57 5\uff09\u6240\u9700\u7684\u6295\u63b7\u6b21\u6570\uff083 \u6b21\uff09\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u8ba1\u7b97\u6bcf\u6b21\u53d1\u5c04\u6210\u529f\u7684\u6982\u7387\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u516d\u79cd\u53ef\u80fd\u7ed3\u679c\u4e2d\u53ea\u6709\u4e00\u79cd\u79ef\u6781\u7ed3\u679c\uff0c\u56e0\u6b64\u6982\u7387<em>p<\/em>\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-d3edc23a0939657deeeed11600ba29be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{1}{6}=0,1667\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"121\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u7136\u540e\u6211\u4eec\u5e94\u7528\u51e0\u4f55\u5206\u5e03\u516c\u5f0f\u6765\u786e\u5b9a\u7ec3\u4e60\u8981\u6c42\u6211\u4eec\u7684\u6982\u7387\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-ceea593841fd847270f92b3ffa919d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle P[X=x]&amp;=(1-p)^{x-1}\\cdot p\\\\[2ex]\\displaystyle P[X=3]&amp;=\\left(1-\\frac{1}{6}\\right)^{3-1}\\cdot \\frac{1}{6}\\\\[2ex]\\displaystyle P[X=3]&amp;=0,1157\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"132\" width=\"216\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-geometrica\"><\/span>\u51e0\u4f55\u5206\u5e03\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u51e0\u4f55\u5206\u5e03\u6ee1\u8db3\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li>\u51e0\u4f55\u5206\u5e03\u6709\u4e00\u4e2a\u7279\u5f81\u53c2\u6570<em>p<\/em> \uff0c\u5b83\u662f\u6bcf\u4e2a\u5b9e\u9a8c\u6210\u529f\u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{c} of each experiment carried out.&lt;\/li&gt;&lt;\/ul&gt;[latex]E[X]=\\cfrac{1}{p}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{c}\nPlease use \\mathaccent for accents in math mode.\nleading text: ...0 &lt;ul&gt;&lt;li&gt; The mean of the general distribution\nPlease use \\mathaccent for accents in math mode.\nleading text: ...&gt;&lt;li&gt; The mean of the geometric distribution\nPlease use \\mathaccent for accents in math mode.\nleading text: ...ne of the geometric distribution is\nPlease use \\mathaccent for accents in math mode.\nleading text: ...the geometric distribution is equal to\nPlease use \\mathaccent for accents in math mode.\nleading text: ...geometric tion is equal to one divided\nPlease use \\mathaccent for accents in math mode.\nleading text: ...st equals one divided by probability\nPlease use \\mathaccent for accents in math mode.\n\n<\/pre>\n<ul>\n<li>\u51e0\u4f55\u5206\u5e03\u7684\u65b9\u5dee\u7b49\u4e8e 1 \u51cf\u53bb<em>p<\/em>\u4e0e<em>p<\/em>\u5e73\u65b9\u7684\u5dee\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-78ed5ca4793c0b8e221669de3e49337f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{1-p}{p^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"128\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li>\u51e0\u4f55\u5206\u5e03\u7684\u8d28\u91cf\u51fd\u6570\u7684\u516c\u5f0f\u4e3a\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-aa3e4c205823e02ce285a5987b818985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X=x]=(1-p)^{x-1}\\cdot p\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u7c7b\u4f3c\u5730\uff0c\u51e0\u4f55\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u7684\u516c\u5f0f\u4e3a\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-88686ff4544e13c6431c27b3fc07076c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X\\leq x]=1-(1-p)^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u51e0\u4f55\u5206\u5e03\u662f\u8d1f\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u7279\u4f8b\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u8fd9\u76f8\u5f53\u4e8e\u53c2\u6570<em>r=1<\/em>\u7684\u8d1f\u4e8c\u9879\u5206\u5e03\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-7dbe3c9fff9b5b54e71dcc2632b2e177_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{BN}(1,p) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ X\\sim\\text{Geom\\'etrica}(p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"390\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/\u8d1f-1-\u4e8c\u9879\u5206\u5e03\/\">\u8d1f\u4e8c\u9879\u5206\u5e03<\/a><br \/><span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5206\u5e03-1\/\">\u4e8c\u9879\u5f0f\u5206\u5e03<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-distribucion-geometrica\"><\/span>\u51e0\u4f55\u5206\u5e03\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c06\u53c2\u6570<em>p<\/em>\u7684\u503c\u548c<em>x<\/em>\u7684\u503c\u8f93\u5165\u5230\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u4e2d\u4ee5\u8ba1\u7b97\u6982\u7387\u3002\u60a8\u9700\u8981\u9009\u62e9\u8981\u8ba1\u7b97\u7684\u6982\u7387\uff0c\u5e76\u4f7f\u7528\u70b9\u4f5c\u4e3a\u5c0f\u6570\u5206\u9694\u7b26\u8f93\u5165\u6570\u5b57\uff0c\u4f8b\u5982 0.1667\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>\u51e0\u4f55\u5206\u5e03\u53c2\u6570<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 QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> <input name=\"prob\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce la probabilidad de \u00e9xito de cada experimento aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"margin-bottom:14px; margin-left:5%\"> <span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span>\u6982\u7387\u8ba1\u7b97\uff1a <\/div>\n<div style=\"margin-bottom:14px; margin-left:10%\"><input name=\"tipoprobabilidad\" type=\"radio\" checked=\"\" value=\"probigual\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-95a78799e4906daa08ea620a942c61bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X=\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"34\" style=\"vertical-align: 0px;\"><\/p>\n<p><input name=\"xigual\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\"><\/div>\n<div style=\"margin-bottom:14px; margin-left:10%\"><input name=\"tipoprobabilidad\" type=\"radio\" value=\"probcolaizquierda\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" 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