{"id":1959,"date":"2021-08-11T21:20:49","date_gmt":"2021-08-11T13:20:49","guid":{"rendered":"https:\/\/blog.francis67.cc\/?p=1959"},"modified":"2022-01-19T00:32:01","modified_gmt":"2022-01-18T16:32:01","slug":"%e5%9d%87%e5%80%bc%e3%80%81%e6%96%b9%e5%b7%ae%e5%92%8c%e5%9d%87%e6%96%b9%e5%80%bc","status":"publish","type":"post","link":"https:\/\/blog.francis67.cc\/?p=1959","title":{"rendered":"\u5747\u503c\u3001\u65b9\u5dee\u548c\u5747\u65b9\u503c"},"content":{"rendered":"\n<p>\u5bf9\u4e8e\u79bb\u6563\u4fe1\u53f7\uff08\u566a\u58f0\uff09 \\( x(i) \\)<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.francis67.cc\/?p=1959\/#%E5%9D%87%E5%80%BC\" >\u5747\u503c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.francis67.cc\/?p=1959\/#%E6%96%B9%E5%B7%AE\" >\u65b9\u5dee<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.francis67.cc\/?p=1959\/#%E5%9D%87%E6%96%B9%E5%80%BC\" >\u5747\u65b9\u503c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.francis67.cc\/?p=1959\/#%E5%9D%87%E5%80%BC%E3%80%81%E6%96%B9%E5%B7%AE%E5%92%8C%E5%9D%87%E6%96%B9%E5%80%BC%E4%B9%8B%E9%97%B4%E7%9A%84%E5%85%B3%E7%B3%BB\" >\u5747\u503c\u3001\u65b9\u5dee\u548c\u5747\u65b9\u503c\u4e4b\u95f4\u7684\u5173\u7cfb<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9D%87%E5%80%BC\"><\/span>\u5747\u503c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p> \\( \\mu_{x} = \\frac{1}{n} \\sum_{i=1}^{n}x(i) \\) \uff0c\u5bf9\u4e8e\u7535\u538b\u6216\u7535\u6d41\u578b\u968f\u673a\u566a\u58f0\uff0c\u5747\u503c \u03bc\u8868\u793a\u5176\u76f4\u6d41\u5206\u91cf<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%96%B9%E5%B7%AE\"><\/span>\u65b9\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p> \\(  \\sigma_{x}^{2} = \\frac{1}{n} \\sum_{i=1}^{n}[x(i)-\\mu _{x}]^{2} \\)\uff0c\u65b9\u5dee\u53cd\u5e94\u968f\u673a\u566a\u58f0\u7684\u8d77\u4f0f\u7a0b\u5ea6<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9D%87%E6%96%B9%E5%80%BC\"><\/span>\u5747\u65b9\u503c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>  \\( \\overline{x^{2}} \\)  \u8868\u793a\u968f\u673a\u566a\u58f0\u77ac\u65f6\u53d6\u503c\u7684\u5e73\u65b9\u7684\u6570\u5b66\u671f\u671b\u503c<\/p>\n\n\n\n<p>\\( \\overline{x^{2}}  \\)\u7684\u5e73\u65b9\u6839\u662f\u968f\u673a\u566a\u58f0\u7684\u6709\u6548\u503c \uff08root mean square\uff0cRMS\uff09<\/p>\n\n\n\n<p> \\( \\overline{x^{2}} = \\frac{1}{n} \\sum_{i=1}^{n}x(i)^{2}   \\) <\/p>\n\n\n\n<p>  \\( RMS = \\sqrt{ \\overline{x^{2}} } = \\sqrt{\\frac{1}{n} \\sum_{i=1}^{n}x(i)^{2}}   \\)  <\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9D%87%E5%80%BC%E3%80%81%E6%96%B9%E5%B7%AE%E5%92%8C%E5%9D%87%E6%96%B9%E5%80%BC%E4%B9%8B%E9%97%B4%E7%9A%84%E5%85%B3%E7%B3%BB\"><\/span>\u5747\u503c\u3001\u65b9\u5dee\u548c\u5747\u65b9\u503c\u4e4b\u95f4\u7684\u5173\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\\(  \\overline{x^{2}} =  \\mu_{x}^{2} +  \\sigma_{x}^{2}   \\)<\/p>\n\n\n\n<p>\u53ef\u4ee5\u770b\u4f5c\u603b\u4f53\u529f\u7387=\u76f4\u6d41\u529f\u7387+\u4ea4\u6d41\u529f\u7387<\/p>\n\n\n\n<p>\u63a8\u5bfc\u53c2\u8003\u671f\u671b\u548c\u65b9\u5dee\u7684\u8054\u7cfb<\/p>\n\n\n\n<p><\/p>\n\n\n\n\\begin{equation} \n\\begin{aligned} \nD[X]&amp;=E[X-E[X]]^2 \\\\\n&amp;=E[X^2-2X\\cdot E[X]+[E[X]]^2]\\\\\n&amp;=E[X^2]-E[2X\\cdot E[X]]+[E[X]]^2\\\\\n&amp;=E[X^2]-2E[X]\\cdot E[X]+[E[X]]^2\\\\\n&amp;=E[X^2]-[E[X]]^2\\\\\n\\end{aligned} \n\\end{equation}\n","protected":false},"excerpt":{"rendered":"<p>\u5bf9\u4e8e\u79bb\u6563\u4fe1\u53f7\uff08\u566a\u58f0\uff09 \\( x(i) \\) \u5747\u503c \\( \\mu_{x} = \\frac{1}{n} \\sum_ [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[338,339,340,342,341],"class_list":["post-1959","post","type-post","status-publish","format-standard","hentry","category-notes","tag-338","tag-339","tag-340","tag-342","tag-341"],"_links":{"self":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts\/1959","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1959"}],"version-history":[{"count":22,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts\/1959\/revisions"}],"predecessor-version":[{"id":2245,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=\/wp\/v2\/posts\/1959\/revisions\/2245"}],"wp:attachment":[{"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1959"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1959"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.francis67.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}