{"id":237,"date":"2023-08-03T19:36:43","date_gmt":"2023-08-03T19:36:43","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%8c%87%e6%95%b0%e5%88%86%e5%b8%83-1\/"},"modified":"2023-08-03T19:36:43","modified_gmt":"2023-08-03T19:36:43","slug":"%e6%8c%87%e6%95%b0%e5%88%86%e5%b8%83-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%8c%87%e6%95%b0%e5%88%86%e5%b8%83-1\/","title":{"rendered":"\u6307\u6570\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u6307\u6570\u5206\u5e03\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u4f1a\u53d1\u73b0\u6307\u6570\u5206\u5e03\u7684\u5c5e\u6027\u53ca\u5176\u516c\u5f0f\u3001\u56fe\u8868\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u4f7f\u7528\u5728\u7ebf\u6307\u6570\u5206\u5e03\u8ba1\u7b97\u5668\u8ba1\u7b97\u4efb\u4f55\u6982\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-exponencial\"><\/span>\u4ec0\u4e48\u662f\u6307\u6570\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6307\u6570\u5206\u5e03<\/strong>\u662f\u4e00\u79cd\u8fde\u7eed\u6982\u7387\u5206\u5e03\uff0c\u7528\u4e8e\u5bf9\u968f\u673a\u73b0\u8c61\u53d1\u751f\u7684\u7b49\u5f85\u65f6\u95f4\u8fdb\u884c\u5efa\u6a21\u3002<\/p>\n<p>\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u6307\u6570\u5206\u5e03\u4f7f\u6211\u4eec\u80fd\u591f\u63cf\u8ff0\u9075\u5faa\u6cca\u677e\u5206\u5e03\u7684\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u7b49\u5f85\u65f6\u95f4\u3002\u56e0\u6b64\uff0c\u6307\u6570\u5206\u5e03\u4e0e\u6cca\u677e\u5206\u5e03\u5bc6\u5207\u76f8\u5173\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\/\u9c7c\u7c7b\u6cd5\/\">\u4ec0\u4e48\u662f\u6cca\u677e\u5206\u5e03\uff1f<\/a><\/div>\n<p>\u6307\u6570\u5206\u5e03\u6709\u4e00\u4e2a\u7279\u5f81\u53c2\u6570\uff0c\u7528\u5e0c\u814a\u5b57\u6bcd \u03bb \u8868\u793a\uff0c\u8868\u793a\u6240\u7814\u7a76\u7684\u4e8b\u4ef6\u5728\u7ed9\u5b9a\u65f6\u95f4\u6bb5\u5185\u9884\u8ba1\u53d1\u751f\u7684\u6b21\u6570\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-05fa833356caeb193384f780ae4edac1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Exp}(\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u540c\u6837\uff0c\u6307\u6570\u5206\u5e03\u4e5f\u7528\u4e8e\u5bf9\u6545\u969c\u53d1\u751f\u4e4b\u524d\u7684\u65f6\u95f4\u8fdb\u884c\u5efa\u6a21\u3002\u56e0\u6b64\uff0c\u6307\u6570\u5206\u5e03\u5728\u53ef\u9760\u6027\u548c\u751f\u5b58\u7406\u8bba\u4e2d\u6709\u591a\u79cd\u5e94\u7528\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-distribuciones-exponenciales\"><\/span>\u6307\u6570\u5206\u5e03\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u6307\u6570\u5206\u5e03\u7684\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u4e00\u4e0b\u8fd9\u79cd\u5206\u5e03\u7684\u51e0\u4e2a\u4f8b\u5b50\uff0c\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n<p><strong><u style=\"text-decoration-color:#FF8A05\">\u6307\u6570\u5206\u5e03\u7684\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;\">\u547c\u53eb\u4e2d\u5fc3\u4e24\u6b21\u547c\u53eb\u4e4b\u95f4\u7ecf\u8fc7\u7684\u65f6\u95f4\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u4e00\u4e2a\u4eba\u5fc5\u987b\u7b49\u5f85\u514d\u8d39\u51fa\u79df\u8f66\u7ecf\u8fc7\u7279\u5b9a\u8857\u9053\u7684\u65f6\u95f4\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u65b0\u987e\u5ba2\u8fdb\u5165\u5546\u5e97\u4e4b\u524d\u7684\u7b49\u5f85\u65f6\u95f4\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u4e24\u4e2a\u4e0d\u540c\u7528\u6237\u8fdb\u5165\u7f51\u9875\u4e4b\u95f4\u6240\u7ecf\u8fc7\u7684\u65f6\u95f4\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u673a\u573a\u4ece\u4e00\u67b6\u98de\u673a\u8d77\u98de\u5230\u53e6\u4e00\u67b6\u98de\u673a\u8d77\u98de\u4e4b\u95f4\u6240\u7ecf\u8fc7\u7684\u65f6\u95f4\u3002<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-exponencial\"><\/span>\u6307\u6570\u5206\u5e03\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5b9a\u4e49\u6307\u6570\u5206\u5e03\u6982\u7387\u8ba1\u7b97\u7684\u5bc6\u5ea6\u51fd\u6570\u516c\u5f0f\u7b49\u4e8e \u03bb \u4e58\u4ee5\u6570\u5b57 e \u7684\u8d1f \u03bb \u6b21\u65b9\u4e58\u4ee5 x\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c<strong>\u6307\u6570\u5206\u5e03\u6982\u7387\u7684\u8ba1\u7b97\u516c\u5f0f<\/strong>\u5982\u4e0b\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-exponentielle.png\" alt=\"\u6307\u6570\u5206\u5e03\u516c\u5f0f\" class=\"wp-image-4891\" width=\"252\" height=\"252\" 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\u6307\u6570\u5206\u5e03\u7684\u6982\u7387\u3002<\/u><\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8ba1\u7b97\u6307\u6570\u5206\u5e03\u7d2f\u79ef\u6982\u7387\u7684\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-ff4b15c1307aa0187d806d3aa9c394d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X\\leq x]=1-e^{-\\lambda x}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-exponencial\"><\/span>\u6307\u6570\u5206\u5e03\u56fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u672c\u8282\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u6307\u6570\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u548c\u5206\u5e03\u51fd\u6570\u7684\u56fe\u5f62\u8868\u793a\u3002<\/p>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u6307\u6570\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u56fe\u5982\u4f55\u6839\u636e\u53c2\u6570 \u03bb \u7684\u503c\u800c\u53d8\u5316\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-graphique-exponentielle.png\" alt=\"\u6307\u6570\u5206\u5e03\u56fe\" class=\"wp-image-4897\" width=\"604\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u540c\u6837\uff0c\u6307\u6570\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u4e5f\u53d6\u51b3\u4e8e\u53c2\u6570 \u03bb \u7684\u503c\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-exponentielle-probabilite-cumulative.png\" alt=\"\u6307\u6570\u7d2f\u79ef\u5206\u5e03\u6982\u7387\u56fe\" class=\"wp-image-4898\" width=\"604\" height=\"395\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-la-distribucion-exponencial\"><\/span>\u89e3\u7b54\u4e86\u6307\u6570\u5206\u5e03\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u5e73\u5747\u800c\u8a00\uff0c\u03bb=1 \u4e2a\u7528\u6237\/\u5206\u949f\u8bbf\u95ee\u7279\u5b9a\u7f51\u9875\u3002\u4e24\u4e2a\u7528\u6237\u8fdb\u5165\u4e4b\u95f4\u7684\u65f6\u95f4\u95f4\u9694\u4e3a 3 \u5206\u949f\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f\u90a3\u4e48\u7b49\u4e8e\u6216\u5c0f\u4e8e2\u5206\u949f\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u5b9a\u4e49\u8be5\u95ee\u9898\u7684\u968f\u673a\u53d8\u91cf\u7684\u5206\u5e03\u662f\u6307\u6570\u5206\u5e03\uff0c\u56e0\u4e3a\u6211\u4eec\u7814\u7a76\u4ece\u4e8b\u4ef6\u53d1\u751f\uff08\u7528\u6237\u8fdb\u5165\u7f51\u9875\uff09\u5230\u540c\u4e00\u4e8b\u4ef6\u518d\u6b21\u53d1\u751f\u6240\u7ecf\u8fc7\u7684\u65f6\u95f4\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-a843576c35aa4a4062a40dfed3da7ffe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Exp}(1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u4e24\u4e2a\u4e0d\u540c\u7528\u6237\u8fdb\u5165\u4e4b\u95f4\u6240\u7ecf\u8fc7\u7684\u65f6\u95f4\u4e3a\u4e09\u5206\u949f\u7684\u6982\u7387\uff0c\u6211\u4eec\u9700\u8981\u5e94\u7528\u5bc6\u5ea6\u51fd\u6570\u516c\u5f0f\uff08\u89c1\u4e0a\u6587\uff09\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-4eb2d6e5190f313d74831763613683ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P[X=x]&amp;=\\lambda e^{-\\lambda x}\\\\[2ex]P[X=3]&amp;=1\\cdot e^{-1\\cdot 3}\\\\[2ex]P[X=3]&amp;=0,05\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"156\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4e3a\u4e86\u786e\u5b9a\u7d2f\u79ef\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u6307\u6570\u5206\u5e03\u7684\u5206\u5e03\u51fd\u6570\u516c\u5f0f\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-5ff6ef636fd31aec708b387669a68b93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P[X\\leq x]&amp;=1- e^{-\\lambda x}\\\\[2ex]P[X\\leq 2]&amp;=1-e^{-1\\cdot 2}\\\\[2ex]P[X\\leq 2]&amp;=0,86\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-exponencial\"><\/span>\u6307\u6570\u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u5206\u5e03\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u6307\u6570\u5206\u5e03\u6709\u4e00\u4e2a\u7279\u5f81\u53c2\u6570 \u03bb\uff0c\u5b83\u8868\u793a\u6240\u7814\u7a76\u7684\u73b0\u8c61\u5728\u7ed9\u5b9a\u65f6\u95f4\u6bb5\u5185\u9884\u8ba1\u53d1\u751f\u7684\u6b21\u6570\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-05fa833356caeb193384f780ae4edac1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Exp}(\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6307\u6570\u5206\u5e03\u4e0d\u80fd\u53d6\u8d1f\u503c\uff0c\u56e0\u6b64\u6307\u6570\u5206\u5e03\u7684\u57df\u7531\u6240\u6709\u5927\u4e8e\u6216\u7b49\u4e8e\u96f6\u7684\u5b9e\u6570\u7ec4\u6210\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-857b41e1aa6e3fc962595eabd52a18e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6307\u6570\u5206\u5e03\u7684\u5e73\u5747\u503c\u7b49\u4e8e\u4e00\u9664\u4ee5\u7279\u5f81\u53c2\u6570 \u03bb\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-6a805fe49674e7a84b44057fbd17dfe4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{1}{\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"77\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6307\u6570\u5206\u5e03\u7684\u65b9\u5dee\u662f\u5176\u5747\u503c\u7684\u5e73\u65b9\uff0c\u56e0\u6b64\u6307\u6570\u5206\u5e03\u7684\u65b9\u5dee\u7b49\u4e8e\u7cfb\u6570 \u03bb \u5e73\u65b9\u7684 1\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-d3e1c6b567a5c0c7f78d58da0920163f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{1}{\\lambda^2 }\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u65e0\u8bba \u03bb \u7684\u503c\u662f\u591a\u5c11\uff0c\u6307\u6570\u5206\u5e03\u7684\u4e0d\u5bf9\u79f0\u7cfb\u6570\u59cb\u7ec8\u7b49\u4e8e 2\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-43776536b020abda26e5455770a96cfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=2\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u540c\u6837\uff0c\u4efb\u4f55\u6307\u6570\u5206\u5e03\u7684\u5cf0\u5ea6\u7cfb\u6570\u59cb\u7ec8\u7b49\u4e8e 9\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-a42692dc0052ffa4b4f5b962b9b7ee8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=9\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6307\u6570\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u7684\u516c\u5f0f\u4e3a\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" 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