{"id":82,"date":"2023-08-05T16:44:39","date_gmt":"2023-08-05T16:44:39","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%95%b0%e5%ad%a6%e6%9c%9f%e6%9c%9b%e6%88%96%e6%9c%9f%e6%9c%9b%e5%80%bc\/"},"modified":"2023-08-05T16:44:39","modified_gmt":"2023-08-05T16:44:39","slug":"%e6%95%b0%e5%ad%a6%e6%9c%9f%e6%9c%9b%e6%88%96%e6%9c%9f%e6%9c%9b%e5%80%bc","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%95%b0%e5%ad%a6%e6%9c%9f%e6%9c%9b%e6%88%96%e6%9c%9f%e6%9c%9b%e5%80%bc\/","title":{"rendered":"\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u968f\u673a\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u5b83\u3002\u4f60\u4f1a\u53d1\u73b0\u6570\u5b66\u5e0c\u671b\u7684\u89e3\u51b3\u65b9\u6848\u3002\u6b64\u5916\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u5728\u7ebf\u8ba1\u7b97\u5668\u627e\u5230\u4efb\u4f55\u6570\u636e\u96c6\u7684\u9884\u671f\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\" id=\"que-es-la-esperanza-matematica-o-valor-esperado\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-esperanza-matematica-o-valor-esperado\"><\/span>\u4ec0\u4e48\u662f\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u671f\u671b\uff08expectation<\/strong> \uff09\uff0c\u4e5f\u79f0\u4e3a<strong>\u671f\u671b\u503c\uff08expected value<\/strong> \uff09\uff0c\u662f\u4e00\u4e2a\u4ee3\u8868\u968f\u673a\u53d8\u91cf\u5e73\u5747\u503c\u7684\u6570\u5b57\u3002\u6570\u5b66\u671f\u671b\u7b49\u4e8e\u968f\u673a\u4e8b\u4ef6\u7684\u503c\u4e0e\u5176\u5404\u81ea\u53d1\u751f\u7684\u6982\u7387\u5f62\u6210\u7684\u6240\u6709\u4e58\u79ef\u4e4b\u548c\u3002<\/p>\n<p>\u671f\u671b\u7684\u7b26\u53f7\u662f\u5927\u5199\u7684E\uff0c\u4f8b\u5982\u7edf\u8ba1\u53d8\u91cfX\u7684\u671f\u671b\u7528E(X)\u8868\u793a\u3002<\/p>\n<p>\u540c\u6837\uff0c\u6570\u636e\u96c6\u7684\u6570\u5b66\u671f\u671b\u503c\u4e0e\u5176\u5e73\u5747\u503c\uff08\u603b\u4f53\u5e73\u5747\u503c\uff09\u4e00\u81f4\u3002 <\/p>\n<h2 class=\"wp-block-heading\" id=\"como-calcular-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"como-calcular-la-esperanza-matematica\"><\/span>\u5982\u4f55\u8ba1\u7b97\u6570\u5b66\u671f\u671b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97\u79bb\u6563\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\uff0c\u5fc5\u987b\u9075\u5faa\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u6bcf\u4e2a\u53ef\u80fd\u4e8b\u4ef6\u4e58\u4ee5\u5176\u53d1\u751f\u7684\u6982\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u4e0a\u4e00\u6b65\u83b7\u5f97\u7684\u6240\u6709\u7ed3\u679c\u76f8\u52a0\u3002<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u83b7\u5f97\u7684\u503c\u662f\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u3002<\/span><\/li>\n<\/ol>\n<p>\u56e0\u6b64\uff0c<strong>\u8ba1\u7b97\u79bb\u6563\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/espoir-mathematiques-valeur-attendue.png\" alt=\"\u6570\u5b66\u671f\u671b\u6216\u671f\u671b\u503c\" class=\"wp-image-1752\" width=\"279\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u96c6\u7684\u671f\u671b\u503c\u3002<\/u><\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u53ea\u6709\u5f53\u968f\u673a\u53d8\u91cf\u662f\u79bb\u6563\u7684\uff08\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff09\u65f6\uff0c\u624d\u80fd\u4f7f\u7528\u4e0a\u8ff0\u516c\u5f0f\u3002\u4f46\u5982\u679c\u53d8\u91cf\u662f\u8fde\u7eed\u7684\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4e0b\u9762\u7684\u516c\u5f0f\u6765\u83b7\u5f97\u6570\u5b66\u671f\u671b\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-c0ecbcb5a0ab0deb8d097268ac2911f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E(X)=\\int_\\mathbb{R} x\\cdot f_x(x) dx \" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"174\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/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-f27dd617611a2ded87c3e79c1ee76fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f_x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u8fde\u7eed\u53d8\u91cf\u7684\u5bc6\u5ea6\u51fd\u6570<\/p>\n<h2 class=\"wp-block-heading\" id=\"ejemplo-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-esperanza-matematica\"><\/span>\u6570\u5b66\u671f\u671b\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u7684\u5b9a\u4e49\uff0c\u4e0b\u9762\u662f\u4e00\u4e2a\u5177\u4f53\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u4e86\u89e3\u8ba1\u7b97\u662f\u5982\u4f55\u5b8c\u6210\u7684\u3002<\/p>\n<ul>\n<li>\u4e00\u4e2a\u4eba\u53c2\u52a0\u4e00\u4e2a\u6e38\u620f\uff0c\u6839\u636e\u63b7\u9ab0\u5b50\u65f6\u51fa\u73b0\u7684\u6570\u5b57\uff0c\u4ed6\u6216\u5979\u53ef\u4ee5\u8d62\u6216\u8f93\u94b1\u3002\u5982\u679c\u63b7\u51fa 1\uff0c\u60a8\u5c06\u8d62\u5f97 800 \u7f8e\u5143\uff1b\u5982\u679c\u63b7\u51fa 2 \u6216 3\uff0c\u60a8\u5c06\u635f\u5931 500 \u7f8e\u5143\uff1b\u5982\u679c\u63b7\u51fa 4\u30015 \u6216 6\uff0c\u60a8\u5c06\u8d62\u5f97 100 \u7f8e\u5143\u3002\u53c2\u4e0e\u4ef7\u683c\u4e3a 50 \u7f8e\u5143\u3002\u60a8\u4f1a\u63a8\u8350\u53c2\u52a0\u8fd9\u4e2a\u6982\u7387\u6e38\u620f\u5417\uff1f<\/li>\n<\/ul>\n<p>\u9996\u5148\u8981\u505a\u7684\u662f\u786e\u5b9a\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u3002\u7531\u4e8e\u9ab0\u5b50\u6709\u516d\u4e2a\u9762\uff0c\u56e0\u6b64\u6eda\u52a8\u4efb\u610f\u6570\u5b57\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-b6f7689a151fef994183ad359ae578b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{obtener un n\\'umero})=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6bcf\u4e2a\u4e8b\u4ef6\u53d1\u751f\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-3ad9bd3479cfff0fd8a669549b972ecb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{ganar }\\$800)=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" style=\"vertical-align: -12px;\"><\/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-cc814922859e0fd0be7476101a6decc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{perder }\\$500)=2\\cdot \\cfrac{1}{6}=\\cfrac{2}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/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-b2a717f65fcc37f0ec7e338271bef523_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{ganar }\\$100)=3\\cdot \\cfrac{1}{6}=\\cfrac{3}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"199\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u6bcf\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\uff0c\u6211\u4eec\u5e94\u7528\u671f\u671b\u7684\u6570\u5b66\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-2634d90a3d741a7681987d3e7f45ebd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E(X)=\\sum_{i=1}^nx_i\\cdot p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"139\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u8ba1\u7b97\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\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-3a7532f7bc4f9a6fc9c367fe2e28d0bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X)=800\\cdot\\cfrac{1}{6}-500\\cdot \\cfrac{2}{6}+100\\cdot\\cfrac{3}{6}=\\$16,67\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"338\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u9884\u671f\u4ef7\u503c\u4f4e\u4e8e\u53c2\u4e0e\u8fd9\u4e2a\u6e38\u620f\u7684\u4ef7\u683c\uff0c\u6240\u4ee5\u6700\u597d\u4e0d\u8981\u73a9\uff0c\u56e0\u4e3a\u4ece\u957f\u8fdc\u6765\u770b\u4f60\u6700\u7ec8\u4f1a\u8d54\u94b1\u3002\u53ef\u80fd\u5982\u679c\u4f60\u53ea\u5728\u8fbe\u52301\u7684\u65f6\u5019\u53c2\u4e0e\uff0c\u90a3\u4e48\u4f60\u5c31\u4f1a\u8d5a\u5927\u94b1\uff0c\u4f46\u957f\u671f\u6765\u770b\uff0c\u4e8f\u635f\u7684\u6982\u7387\u5f88\u9ad8\u3002<\/p>\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u6570\u5b66\u671f\u671b\u7684\u7ed3\u679c\u6709\u65f6\u662f\u4e00\u4e2a\u4e0d\u53ef\u80fd\u7684\u503c\uff0c\u4f8b\u5982\u672c\u4f8b\u4e2d\u65e0\u6cd5\u5f97\u5230$16.67\u3002 <\/p>\n<h2 class=\"wp-block-heading\" id=\"calculadora-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-esperanza-matematica\"><\/span>\u671f\u671b\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u4e2d\u8f93\u5165\u4e00\u7ec4\u7edf\u8ba1\u6570\u636e\u6765\u8ba1\u7b97\u671f\u671b\u503c\u3002\u60a8\u5fc5\u987b\u5c06\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u503c\u653e\u5165\u7b2c\u4e00\u4e2a\u6846\u4e2d\uff0c\u5e76\u5c06\u5176\u53d1\u751f\u7684\u6982\u7387\u4ee5\u76f8\u540c\u7684\u987a\u5e8f\u653e\u5165\u7b2c\u4e8c\u4e2a\u6846\u4e2d\u3002<\/p>\n<p>\u6570\u636e\u5fc5\u987b\u7528\u7a7a\u683c\u5206\u9694\uff0c\u5e76\u4f7f\u7528\u53e5\u70b9\u4f5c\u4e3a\u5c0f\u6570\u70b9\u5206\u9694\u7b26\u8f93\u5165\u3002<\/p>\n<form action=\"\" method=\"post\">\n<ul>\n<li>\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u4ef7\u503c\uff1a <\/li>\n<\/ul>\n<p><textarea name=\"datosX\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"3 4 1 7 5 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los valores de los sucesos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li>\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\uff1a <\/li>\n<\/ul>\n<p><textarea name=\"datosP\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"0.1 0.25 0.4 0.05 0.15 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce las probabilidades aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u8ba1\u7b97\u6570\u5b66\u671f\u671b\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\" id=\"propiedades-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-esperanza-matematica\"><\/span>\u6570\u5b66\u671f\u671b\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6570\u5b66\u671f\u671b\u7684\u6027\u8d28\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u5e38\u6570\u7684\u6570\u5b66\u671f\u671b\u5c31\u662f\u5b83\u672c\u8eab\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-564923a9300f678924c2bf5d02fb5821_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(k)=k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u968f\u673a\u53d8\u91cf\u7684\u671f\u671b\u4e58\u4ee5\u6807\u91cf\u7b49\u4e8e\u8be5\u53d8\u91cf\u7684\u671f\u671b\u4e58\u4ee5\u8be5\u6807\u91cf\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-506787cf97f31936eef0579d1471a5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(k\\cdot X)=k\\cdot E(X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e24\u4e2a\u53d8\u91cf\u4e4b\u548c\u7684\u6570\u5b66\u671f\u671b\u7b49\u4e8e\u6bcf\u4e2a\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\u4e4b\u548c\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-3cfd9f255e02675ec64ec472d0c997c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X+Y)=E(X)+E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e00\u822c\u6765\u8bf4\uff0c\u4e24\u4e2a\u53d8\u91cf\u76f8\u4e58\u4f1a\u4ea7\u751f\u4e0d\u540c\u7684\u6570\u5b66\u671f\u671b\u3002\u4ec5\u5f53\u53d8\u91cf\u72ec\u7acb\u65f6\uff0c\u7ed3\u679c\u624d\u76f8\u540c\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-116cfab17848d8aa4a3833600bd3215a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X\\cdot Y)\\neq E(X)\\cdot E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u4e00\u4e2a\u53d8\u91cf\u7684\u6240\u6709\u503c\u90fd\u5927\u4e8e\u6216\u7b49\u4e8e\u96f6\uff0c\u90a3\u4e48\u8be5\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\u4e5f\u4e3a\u6b63\u6216\u7b49\u4e8e\u96f6\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-4830aa6f68f621f7bac3ffa0b2d8d2db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\geq 0 \\ \\longrightarrow \\ E(X)\\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"175\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u4e00\u4e2a\u53d8\u91cf\u7684\u6240\u6709\u503c\u90fd\u5c0f\u4e8e\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u6240\u6709\u503c\uff0c\u5219\u4e24\u4e2a\u53d8\u91cf\u7684\u671f\u671b\u5177\u6709\u76f8\u540c\u7684\u5173\u7cfb\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-f236222136aa7e5cab6ff999cfbecb9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\leq Y \\ \\longrightarrow \\ E(X)\\leq E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u6211\u4eec\u77e5\u9053\u4e00\u4e2a\u53d8\u91cf\u53d7\u4e24\u4e2a\u503c\u7684\u9650\u5236\uff0c\u90a3\u4e48\u5b83\u7684\u6570\u5b66\u671f\u671b\u5728\u903b\u8f91\u4e0a\u4e5f\u662f\u6709\u9650\u7684\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-f1241572e77188af4dbd932f7415c0dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\n\n<ul>\n<li> Si une variable est la combinaison lin\u00e9aire d&#8217;une autre variable, ses attentes math\u00e9matiques satisfont \u00e0 la m\u00eame relation alg\u00e9brique : <\/li>\n<\/ul>\n<p>[latex]Y=a+bX \\ \\longrightarrow \\ E(Y)=a+b\\cdot E(X)&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;41&#8243; width=&#8221;1116&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" id=\"para-que-sirve-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"%c2%bfpara-que-sirve-la-esperanza-matematica\"><\/span>\u6570\u5b66\u671f\u671b\u6709\u4ec0\u4e48\u7528\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6700\u540e\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u66f4\u6df1\u5165\u5730\u63a2\u8ba8\u6570\u5b66\u5e0c\u671b\u7684\u542b\u4e49\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u8fd9\u4e2a\u7edf\u8ba1\u6307\u6807\u7684\u7528\u9014\uff0c\u4ece\u800c\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n<p>\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u7528\u4e8e\u8868\u793a\u5728\u6982\u7387\u7a7a\u95f4\u4e2d\u957f\u671f\u9884\u671f\u83b7\u5f97\u6216\u635f\u5931\u7684\u91d1\u989d\u7684\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6570\u5b66\u671f\u671b\u8868\u793a\u957f\u671f\u5c06\u83b7\u5f97\u7684\u56de\u62a5\u3002<\/p>\n<p>\u5f53\u4e00\u4e2a\u4eba\u8003\u8651\u8fdb\u884c\u6295\u8d44\u65f6\uff0c\u4f8b\u5982\u8d2d\u4e70\u4e00\u5bb6\u516c\u53f8\u7684\u80a1\u7968\uff0c\u8981\u8003\u8651\u7684\u53c2\u6570\u4e4b\u4e00\u662f\u6570\u5b66\u671f\u671b\u3002\u56e0\u4e3a\u5982\u679c\u4f60\u591a\u6b21\u8fdb\u884c\u8fd9\u9879\u6295\u8d44\uff0c\u4f60\u5c06\u83b7\u5f97\u7684\u7ecf\u6d4e\u56de\u62a5\u5c06\u662f\u6570\u5b66\u671f\u671b\u503c\u3002\u5b83\u53ef\u4ee5\u88ab\u89c6\u4e3a\u6240\u83b7\u5f97\u7684\u6536\u76ca\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p>\u540c\u6837\uff0c\u6570\u5b66\u671f\u671b\u4e5f\u5e94\u7528\u4e8e\u5176\u4ed6\u9886\u57df\uff0c\u5982\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u3001\u91cf\u5b50\u7269\u7406\u3001\u4ea4\u6613\u751a\u81f3\u751f\u7269\u5b66\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u968f\u673a\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u5b83\u3002\u4f60\u4f1a\u53d1\u73b0\u6570\u5b66\u5e0c\u671b\u7684\u89e3\u51b3\u65b9\u6848\u3002\u6b64\u5916\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u5728\u7ebf\u8ba1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-82","post","type-post","status-publish","format-standard","hentry","category-12"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09<\/title>\n<meta name=\"description\" content=\"\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u968f\u673a\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\uff08\u6216\u671f\u671b\u503c\uff09\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u5b83\u3002\u4f60\u4f1a\u53d1\u73b0\u6570\u5b66\u5e0c\u671b\u7684\u89e3\u51b3\u65b9\u6848\u3002\u6b64\u5916\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u5728\u7ebf\u8ba1\u7b97\u5668\u627e\u5230\u4efb\u4f55\u6570\u636e\u96c6\u7684\u9884\u671f\u503c\u3002\" \/>\n<meta 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