{"id":78,"date":"2023-08-05T17:37:55","date_gmt":"2023-08-05T17:37:55","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/"},"modified":"2023-08-05T17:37:55","modified_gmt":"2023-08-05T17:37:55","slug":"%e5%8d%8f%e6%96%b9%e5%b7%ae","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/","title":{"rendered":"\u534f\u65b9\u5dee"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u534f\u65b9\u5dee\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002\u60a8\u5c06\u627e\u5230\u534f\u65b9\u5dee\u516c\u5f0f\u4ee5\u53ca\u8ba1\u7b97\u6570\u636e\u96c6\u534f\u65b9\u5dee\u7684\u793a\u4f8b\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u4f7f\u7528\u6700\u540e\u7684\u5728\u7ebf\u8ba1\u7b97\u5668\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u7cfb\u5217\u7684\u534f\u65b9\u5dee\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-covarianza\"><\/span>\u4ec0\u4e48\u662f\u534f\u65b9\u5dee\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u534f\u65b9\u5dee<\/strong>\u662f\u8868\u793a\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u8054\u5408\u53d8\u5f02\u7a0b\u5ea6\u7684\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u534f\u65b9\u5dee\u7528\u4e8e\u5206\u6790\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002<\/p>\n<p>\u534f\u65b9\u5dee\u7b49\u4e8e\u4e24\u4e2a\u53d8\u91cf\u7684\u6570\u636e\u4e0e\u5176\u5404\u81ea\u5747\u503c\u4e4b\u5dee\u7684\u4e58\u79ef\u4e4b\u548c\u9664\u4ee5\u6570\u636e\u603b\u6570\u3002 <\/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\/covariance.png\" alt=\"\u534f\u65b9\u5dee\" class=\"wp-image-1610\" width=\"301\" height=\"191\" 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\u534f\u65b9\u5dee\u3002<\/u><\/p>\n<p>\u534f\u65b9\u5dee\u503c\u7684\u89e3\u91ca\u975e\u5e38\u7b80\u5355\uff1a<\/p>\n<ul>\n<li>\u5982\u679c<strong>\u534f\u65b9\u5dee\u4e3a\u6b63<\/strong>\uff0c\u5219\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u76f8\u5173\u6027\u3002\u56e0\u6b64\uff0c\u5f53\u4e00\u4e2a\u53d8\u91cf\u7684\u503c\u589e\u52a0\u65f6\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u4e5f\u4f1a\u589e\u52a0\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002<\/li>\n<li>\u5982\u679c<strong>\u534f\u65b9\u5dee\u4e3a\u8d1f<\/strong>\uff0c\u5219\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u4e3a\u8d1f\u3002\u56e0\u6b64\uff0c\u5f53\u4e00\u4e2a\u53d8\u91cf\u7684\u503c\u589e\u52a0\u65f6\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u503c\u5c31\u4f1a\u51cf\u5c11\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002<\/li>\n<li>\u5982\u679c<strong>\u534f\u65b9\u5dee\u4e3a\u96f6<\/strong>\uff08\u6216\u5176\u503c\u63a5\u8fd1\u96f6\uff09\uff0c\u5219\u610f\u5473\u7740\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u4e0d\u5b58\u5728\u5173\u7cfb\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u662f\u72ec\u7acb\u7684\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-covarianza\"><\/span>\u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97\u6570\u636e\u7cfb\u5217\u7684\u534f\u65b9\u5dee\uff0c\u5fc5\u987b\u6267\u884c\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;\">\u5206\u522b\u8ba1\u7b97\u6bcf\u4e2a\u53d8\u91cf\u7684\u5e73\u5747\u503c\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5bf9\u4e8e\u6bcf\u4e2a\u53d8\u91cf\uff0c\u6c42\u5176\u6bcf\u4e2a\u503c\u4e0e\u8be5\u53d8\u91cf\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u5c06\u6bcf\u4e2a\u6570\u636e\u70b9\u5728\u4e0a\u4e00\u6b65\u4e2d\u8ba1\u7b97\u51fa\u7684\u5dee\u5f02\u76f8\u4e58\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;\">\u9664\u4ee5\u6570\u636e\u603b\u6570\u3002\u83b7\u5f97\u7684\u503c\u662f\u6570\u636e\u5e8f\u5217\u7684\u534f\u65b9\u5dee\u3002<\/span><\/li>\n<\/ol>\n<p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u8ba1\u7b97\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u534f\u65b9\u5dee\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-6e8484a2dfa35044eae76362ca631df2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)=\\cfrac{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})(y_i-\\overline{y})}{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"257\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5f3a\u70c8\u63a8\u8350\u7684\u63d0\u53d6\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u534f\u65b9\u5dee\u7684\u65b9\u6cd5\u662f\u521b\u5efa\u4e00\u4e2a\u5305\u542b\u6240\u6709\u6570\u636e\u5bf9\u7684\u8868\uff0c\u5e76\u4e3a\u4e0a\u8ff0\u6bcf\u4e2a\u6b65\u9aa4\u6dfb\u52a0\u4e00\u5217\u3002\u8fd9\u6837\u4f60\u7684\u8ba1\u7b97\u5c31\u4f1a\u53d8\u5f97\u66f4\u597d\uff0c\u4f60\u4e5f\u4f1a\u66f4\u597d\u5730\u7406\u89e3\u4f60\u5728\u505a\u4ec0\u4e48\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-covarianza\"><\/span>\u534f\u65b9\u5dee\u8ba1\u7b97\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u534f\u65b9\u5dee\u7684\u5b9a\u4e49\uff0c\u4e0b\u9762\u662f\u8ba1\u7b97\u6b64\u7c7b\u7edf\u8ba1\u5ea6\u91cf\u7684\u5206\u6b65\u793a\u4f8b\u3002\u76ee\u7684\u662f\u8ba9\u60a8\u66f4\u597d\u5730\u7406\u89e3\u534f\u65b9\u5dee\u7684\u6982\u5ff5\u4ee5\u53ca\u5982\u4f55\u5206\u6790\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002<\/p>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u7edf\u8ba1\u6570\u636e\u96c6\u7684\u534f\u65b9\u5dee\uff1a <\/li>\n<\/ul>\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\/exemple-donnees-variables-aleatoires.png\" alt=\"\" class=\"wp-image-1612\" width=\"116\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u53d8\u91cf\u7684\u7b97\u672f\u5e73\u5747\u503c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u6bcf\u4e2a\u53d8\u91cf\u503c\u7684\u603b\u548c\u9664\u4ee5\u6570\u636e\u603b\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-4cbd143f38881aba1c648a4d6f306adf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=\\cfrac{58}{10}=5,8\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"103\" 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-a19af98b2edc689420b116d93fffbe6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}=\\cfrac{51}{10}=5,1\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"101\" style=\"vertical-align: -12px;\"><\/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>\u53c2\u89c1\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u7b97\u672f\u5e73\u5747\u6570\/\">\u7b97\u672f\u516c\u5f0f\u5e73\u5747\u503c<\/a><\/div>\n<p>\u4e00\u65e6\u6211\u4eec\u786e\u5b9a\u4e86\u6bcf\u4e2a\u968f\u673a\u53d8\u91cf\u7684\u5747\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06\u4ee5\u4e0b\u5217\u6dfb\u52a0\u5230\u6570\u636e\u8868\u4e2d\u4ee5\u83b7\u5f97\u534f\u65b9\u5dee\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\/exercice-de-covariance-resolu.png\" alt=\"\u534f\u65b9\u5dee\u7ec3\u4e60\u5df2\u89e3\u51b3\" class=\"wp-image-1614\" width=\"376\" height=\"287\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u8981\u786e\u5b9a\u4e24\u4e2a\u53d8\u91cf\u7684\u534f\u65b9\u5dee\uff0c\u60a8\u5fc5\u987b\u5c06\u6700\u540e\u4e00\u5217\u7684\u603b\u548c\u9664\u4ee5\u6570\u636e\u5bf9\u7684\u6570\u91cf\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-49b4992f8443e4d94e38dfa56da38a9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}Cov(X,Y)&amp;=\\cfrac{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})(y_i-\\overline{y})}{n}\\\\[2ex] Cov(X,Y)&amp;= \\cfrac{41,2}{10} \\\\[2ex]Cov(X,Y)&amp;= 4,12\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"175\" width=\"257\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u534f\u65b9\u5dee\u503c\u4e3a\u6b63\uff0c\u8fd9\u610f\u5473\u7740\u6240\u7814\u7a76\u7684\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u76f4\u63a5\u4f9d\u8d56\u6027\u3002\u7136\u800c\uff0c\u5982\u679c\u534f\u65b9\u5dee\u503c\u4e3a\u8d1f\uff0c\u5219\u610f\u5473\u7740\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u662f\u76f8\u53cd\u7684\u3002\u6700\u540e\uff0c\u5982\u679c\u534f\u65b9\u5dee\u503c\u4e3a\u96f6\u6216\u975e\u5e38\u63a5\u8fd1\u96f6\uff0c\u5219\u610f\u5473\u7740\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u4e0d\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\u3002<\/p>\n<p>\u4ece\u6c42\u89e3\u6b64\u793a\u4f8b\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u4f7f\u7528 Excel \u7b49\u8ba1\u7b97\u673a\u7a0b\u5e8f\u5c06\u5217\u6dfb\u52a0\u5230\u8868\u4e2d\u5e76\u5feb\u901f\u6267\u884c\u8ba1\u7b97\u975e\u5e38\u6709\u7528\u3002\u5426\u5219\uff0c\u901a\u8fc7\u624b\u52a8\u8ba1\u7b97\u8fd0\u7b97\uff0c\u627e\u5230\u534f\u65b9\u5dee\u9700\u8981\u66f4\u957f\u7684\u65f6\u95f4\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-covarianza\"><\/span>\u534f\u65b9\u5dee\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\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u3002\u60a8\u9700\u8981\u5206\u9694\u6570\u636e\u5bf9\uff0c\u4ee5\u4fbf\u7b2c\u4e00\u4e2a\u6846\u4e2d\u53ea\u6709\u4e00\u4e2a\u53d8\u91cf\u7684\u503c\uff0c\u7b2c\u4e8c\u4e2a\u6846\u4e2d\u53ea\u6709\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u7684\u503c\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>\u968f\u673a\u53d8\u91cf<\/li>\n<\/ul>\n<p><textarea name=\"datosX\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"1 4 8 5 7.2 9 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos de la primera variable aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li>\u968f\u673a\u53d8\u91cf Y\uff1a <\/li>\n<\/ul>\n<p><textarea name=\"datosY\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"2 5 7 3 2 1 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos de la segunda variable 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\u534f\u65b9\u5dee\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-covarianza\"><\/span>\u534f\u65b9\u5dee\u5c5e\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u534f\u65b9\u5dee\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<ul>\n<li>\u968f\u673a\u53d8\u91cf\u548c\u5e38\u6570\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u4e3a\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-3521edd5d0781593491d07e147d9274e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,a)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u53d8\u91cf\u4e0e\u5176\u81ea\u8eab\u7684\u534f\u65b9\u5dee\u7b49\u4e8e\u8be5\u53d8\u91cf\u7684\u65b9\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-b96c9e198a0904a56206dedad0e7608c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,X)=Var(X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" 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>\u770b\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\/\">\u4ec0\u4e48\u662f\u65b9\u5dee\uff1f<\/a><\/div>\n<ul>\n<li>\u534f\u65b9\u5dee\u6ee1\u8db3\u5bf9\u79f0\u6027\uff0c\u56e0\u6b64\u53d8\u91cfX\u548cY\u7684\u534f\u65b9\u5dee\u7b49\u4e8e\u53d8\u91cfY\u548cX\u7684\u534f\u65b9\u5dee\u3002\u53d8\u91cf\u7684\u987a\u5e8f\u4e0d\u5f71\u54cd\u534f\u65b9\u5dee\u7684\u7ed3\u679c\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-0d384166725954287d0065f3a145c61a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)=Cov(Y,X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u53d8\u91cf\u4e58\u4ee5\u5e38\u6570\uff0c\u53ef\u4ee5\u5148\u8ba1\u7b97\u534f\u65b9\u5dee\uff0c\u7136\u540e\u5c06\u7ed3\u679c\u4e58\u4ee5\u5e38\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-2ea811783444fab37858b563c94c0ce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(a\\cdot X,b\\cdot Y)=a\\cdot b\\cdot Cov(X,Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"273\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5411\u53d8\u91cf\u6dfb\u52a0\u9879\u4e0d\u4f1a\u5f71\u54cd\u534f\u65b9\u5dee\u7ed3\u679c\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-2fa1b5d5152dd55933384887aea08396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(a+X,b+Y)=Cov(X+Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"263\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u4e0e\u5176\u6570\u5b66\u671f\u671b\u6709\u5173\u3002\u53d8\u91cfX\u548cY\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u7b49\u4e8eX\u548cY\u4e58\u79ef\u7684\u6570\u5b66\u671f\u671b\u51cf\u53bb\u6bcf\u4e2a\u53d8\u91cf\u7684\u6570\u5b66\u671f\u671b\u7684\u4e58\u79ef\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-5cdc964b9ce9f0c87cf3fd8fc5eb84fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)=E[X\\cdot Y]-E[X]\\cdot E[Y]\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"284\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5f53\u4f7f\u7528\u53d8\u91cf\u8fdb\u884c\u64cd\u4f5c\u65f6\uff0c\u4e0b\u9762\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u662f\u5173\u4e8e\u534f\u65b9\u5dee\u7684\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-5d429b5bb4e4796cc5b8c73ed0845fa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle Cov(aX+bY,cW+dV)= \\ &amp; \\displaystyle acCov(X,W)+adCov(X,V)+\\\\[2ex]&amp; +bcCov(Y,W)+bdCov(Y,V)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"457\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u534f\u65b9\u5dee\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002\u60a8\u5c06\u627e\u5230\u534f\u65b9\u5dee\u516c\u5f0f\u4ee5\u53ca\u8ba1\u7b97\u6570\u636e\u96c6\u534f\u65b9\u5dee\u7684\u793a\u4f8b\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u4f7f\u7528\u6700\u540e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-78","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u534f\u65b9\u5dee\uff1a\u516c\u5f0f\u3001\u793a\u4f8b\u3001\u5c5e\u6027\u3001\u8ba1\u7b97\u5668...<\/title>\n<meta name=\"description\" content=\"\u534f\u65b9\u5dee\u7684\u5b9a\u4e49 - \u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u516c\u5f0f\uff09 - \u5b9e\u9645\u793a\u4f8b - \u534f\u65b9\u5dee\u8ba1\u7b97\u5668 - \u534f\u65b9\u5dee\u7684\u6027\u8d28\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u534f\u65b9\u5dee\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 \u534f\u65b9\u5dee\uff1a\u516c\u5f0f\u3001\u793a\u4f8b\u3001\u5c5e\u6027\u3001\u8ba1\u7b97\u5668...\" \/>\n<meta property=\"og:description\" content=\"\u534f\u65b9\u5dee\u7684\u5b9a\u4e49 - \u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u516c\u5f0f\uff09 - \u5b9e\u9645\u793a\u4f8b - \u534f\u65b9\u5dee\u8ba1\u7b97\u5668 - \u534f\u65b9\u5dee\u7684\u6027\u8d28\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/cn\/\u534f\u65b9\u5dee\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-05T17:37:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/covariance.png\" \/>\n<meta name=\"author\" content=\"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/\",\"url\":\"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/\",\"name\":\"\u25b7 \u534f\u65b9\u5dee\uff1a\u516c\u5f0f\u3001\u793a\u4f8b\u3001\u5c5e\u6027\u3001\u8ba1\u7b97\u5668...\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/cn\/#website\"},\"datePublished\":\"2023-08-05T17:37:55+00:00\",\"dateModified\":\"2023-08-05T17:37:55+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/cn\/#\/schema\/person\/124e4e5b7c9f8dc0f1f95cc8c1db3261\"},\"description\":\"\u534f\u65b9\u5dee\u7684\u5b9a\u4e49 - \u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u516c\u5f0f\uff09 - \u5b9e\u9645\u793a\u4f8b - \u534f\u65b9\u5dee\u8ba1\u7b97\u5668 - \u534f\u65b9\u5dee\u7684\u6027\u8d28\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u5bb6\",\"item\":\"https:\/\/statorials.org\/cn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u534f\u65b9\u5dee\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/cn\/#website\",\"url\":\"https:\/\/statorials.org\/cn\/\",\"name\":\"Statorials\",\"description\":\"\u60a8\u7684\u7edf\u8ba1\u7d20\u517b\u6307\u5357\uff01\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/cn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/cn\/#\/schema\/person\/124e4e5b7c9f8dc0f1f95cc8c1db3261\",\"name\":\"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/statorials.org\/cn\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/cn\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/cn\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a\"},\"description\":\"\u5927\u5bb6\u597d\uff0c\u6211\u662f\u672c\u6770\u660e\uff0c\u4e00\u4f4d\u9000\u4f11\u7684\u7edf\u8ba1\u5b66\u6559\u6388\uff0c\u540e\u6765\u6210\u4e3a Statorials \u7684\u70ed\u5fc3\u6559\u5e08\u3002 \u51ed\u501f\u5728\u7edf\u8ba1\u9886\u57df\u7684\u4e30\u5bcc\u7ecf\u9a8c\u548c\u4e13\u4e1a\u77e5\u8bc6\uff0c\u6211\u6e34\u671b\u5206\u4eab\u6211\u7684\u77e5\u8bc6\uff0c\u901a\u8fc7 Statorials \u589e\u5f3a\u5b66\u751f\u7684\u80fd\u529b\u3002\u4e86\u89e3\u66f4\u591a\",\"sameAs\":[\"https:\/\/statorials.org\/cn\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 \u534f\u65b9\u5dee\uff1a\u516c\u5f0f\u3001\u793a\u4f8b\u3001\u5c5e\u6027\u3001\u8ba1\u7b97\u5668...","description":"\u534f\u65b9\u5dee\u7684\u5b9a\u4e49 - \u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u516c\u5f0f\uff09 - \u5b9e\u9645\u793a\u4f8b - \u534f\u65b9\u5dee\u8ba1\u7b97\u5668 - \u534f\u65b9\u5dee\u7684\u6027\u8d28","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/cn\/\u534f\u65b9\u5dee\/","og_locale":"zh_CN","og_type":"article","og_title":"\u25b7 \u534f\u65b9\u5dee\uff1a\u516c\u5f0f\u3001\u793a\u4f8b\u3001\u5c5e\u6027\u3001\u8ba1\u7b97\u5668...","og_description":"\u534f\u65b9\u5dee\u7684\u5b9a\u4e49 - \u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u516c\u5f0f\uff09 - \u5b9e\u9645\u793a\u4f8b - \u534f\u65b9\u5dee\u8ba1\u7b97\u5668 - \u534f\u65b9\u5dee\u7684\u6027\u8d28","og_url":"https:\/\/statorials.org\/cn\/\u534f\u65b9\u5dee\/","og_site_name":"Statorials","article_published_time":"2023-08-05T17:37:55+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/covariance.png"}],"author":"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/","url":"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/","name":"\u25b7 \u534f\u65b9\u5dee\uff1a\u516c\u5f0f\u3001\u793a\u4f8b\u3001\u5c5e\u6027\u3001\u8ba1\u7b97\u5668...","isPartOf":{"@id":"https:\/\/statorials.org\/cn\/#website"},"datePublished":"2023-08-05T17:37:55+00:00","dateModified":"2023-08-05T17:37:55+00:00","author":{"@id":"https:\/\/statorials.org\/cn\/#\/schema\/person\/124e4e5b7c9f8dc0f1f95cc8c1db3261"},"description":"\u534f\u65b9\u5dee\u7684\u5b9a\u4e49 - \u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u516c\u5f0f\uff09 - \u5b9e\u9645\u793a\u4f8b - \u534f\u65b9\u5dee\u8ba1\u7b97\u5668 - \u534f\u65b9\u5dee\u7684\u6027\u8d28","breadcrumb":{"@id":"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/cn\/%e5%8d%8f%e6%96%b9%e5%b7%ae\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u5bb6","item":"https:\/\/statorials.org\/cn\/"},{"@type":"ListItem","position":2,"name":"\u534f\u65b9\u5dee"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/cn\/#website","url":"https:\/\/statorials.org\/cn\/","name":"Statorials","description":"\u60a8\u7684\u7edf\u8ba1\u7d20\u517b\u6307\u5357\uff01","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/cn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/statorials.org\/cn\/#\/schema\/person\/124e4e5b7c9f8dc0f1f95cc8c1db3261","name":"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/statorials.org\/cn\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/cn\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/cn\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","caption":"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a"},"description":"\u5927\u5bb6\u597d\uff0c\u6211\u662f\u672c\u6770\u660e\uff0c\u4e00\u4f4d\u9000\u4f11\u7684\u7edf\u8ba1\u5b66\u6559\u6388\uff0c\u540e\u6765\u6210\u4e3a Statorials \u7684\u70ed\u5fc3\u6559\u5e08\u3002 \u51ed\u501f\u5728\u7edf\u8ba1\u9886\u57df\u7684\u4e30\u5bcc\u7ecf\u9a8c\u548c\u4e13\u4e1a\u77e5\u8bc6\uff0c\u6211\u6e34\u671b\u5206\u4eab\u6211\u7684\u77e5\u8bc6\uff0c\u901a\u8fc7 Statorials \u589e\u5f3a\u5b66\u751f\u7684\u80fd\u529b\u3002\u4e86\u89e3\u66f4\u591a","sameAs":["https:\/\/statorials.org\/cn"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/posts\/78","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/comments?post=78"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/posts\/78\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/media?parent=78"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/categories?post=78"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/cn\/wp-json\/wp\/v2\/tags?post=78"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}