{"id":36,"date":"2023-08-06T10:13:35","date_gmt":"2023-08-06T10:13:35","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e9%a2%91%e7%8e%87%e6%a6%82%e7%8e%87-1\/"},"modified":"2023-08-06T10:13:35","modified_gmt":"2023-08-06T10:13:35","slug":"%e9%a2%91%e7%8e%87%e6%a6%82%e7%8e%87-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e9%a2%91%e7%8e%87%e6%a6%82%e7%8e%87-1\/","title":{"rendered":"\u9891\u7387\u6982\u7387\uff08\u6216\u9891\u7387\u4e3b\u4e49\u8005\uff09"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u5b83\u662f\u4ec0\u4e48\u4ee5\u53ca\u5982\u4f55\u8ba1\u7b97\u9891\u7387\u6982\u7387\uff08\u6216\u9891\u7387\u6982\u7387\uff09\u3002\u60a8\u5c06\u627e\u5230\u9891\u7387\u6982\u7387\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9891\u7387\u6982\u7387\u548c\u7406\u8bba\u6982\u7387\u4e4b\u95f4\u7684\u533a\u522b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-frecuencial\"><\/span>\u4ec0\u4e48\u662f\u9891\u7387\u6982\u7387\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u9891\u7387\u6982\u7387<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u9891\u7387\u6982\u7387<\/strong>\uff0c\u662f\u968f\u673a\u5b9e\u9a8c\u4e2d\u57fa\u672c\u4e8b\u4ef6\u7684\u957f\u671f\u9884\u671f\u76f8\u5bf9\u9891\u7387\u3002<\/p>\n<p>\u4e3a\u4e86\u8ba1\u7b97\u4e8b\u4ef6\u53d1\u751f\u7684\u9891\u7387\u6982\u7387\uff0c\u5fc5\u987b\u8fdb\u884c\u5927\u91cf\u5b9e\u9a8c\uff0c\u5e76\u5c06\u83b7\u5f97\u7684\u6709\u5229\u6848\u4f8b\u6570\u9664\u4ee5\u6240\u8fdb\u884c\u7684\u91cd\u590d\u603b\u6570\u3002<\/p>\n<p>\u5b9e\u9a8c\u91cd\u590d\u6b21\u6570\u8d8a\u591a\uff0c\u83b7\u5f97\u7684\u9891\u7387\u6982\u7387\u5c31\u8d8a\u7cbe\u786e\u3002\u56e0\u6b64\uff0c\u8fd9\u79cd\u7c7b\u578b\u7684\u6982\u7387\u901a\u5e38\u662f\u4f7f\u7528\u6a21\u62df\u6570\u5343\u6b21\u8fed\u4ee3\u7684\u8ba1\u7b97\u673a\u7a0b\u5e8f\u6765\u8ba1\u7b97\u7684\uff0c\u5e76\u4e14\u80fd\u591f\u5728\u5f88\u77ed\u7684\u65f6\u95f4\u5185\u5bf9\u5176\u8fdb\u884c\u5206\u6790\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u6765\u8bf4\uff0c\u9891\u7387\u6982\u7387\u516c\u5f0f\u662f<em>N<\/em>\u5728\u65e0\u7a77\u5927<em>s<\/em>\u5904\u7684\u6781\u9650\u9664\u4ee5<em>N<\/em> \uff0c\u5176\u4e2d<em>N<\/em>\u662f\u5b9e\u9a8c\u603b\u6570\uff0c <em>s \u662f<\/em>\u83b7\u5f97\u7684\u6709\u5229\u6848\u4f8b\u7684\u6570\u91cf\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-9ee8cdba2713256ce199da17fcb2235c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(s)=\\lim\\limits_{N\\to \\infty}\\cfrac{s}{N}\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"121\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u60a8\u4e0d\u7406\u89e3\u516c\u5f0f\uff0c\u8bf7\u4e0d\u8981\u62c5\u5fc3\uff0c\u56e0\u4e3a\u4e0d\u53ef\u80fd\u65e0\u9650\u6b21\u5730\u91cd\u590d\u76f8\u540c\u7684\u5b9e\u9a8c\uff0c\u56e0\u4e3a\u6211\u4eec\u6c38\u8fdc\u4e0d\u4f1a\u5b8c\u6210\u5b83\u3002\u8fd9\u662f\u6307\u5fc5\u987b\u8ba1\u7b97\u5927\u91cf\u91cd\u590d\u7684\u9891\u7387\u6982\u7387\u3002<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u9891\u7387\u6982\u7387\u662f\u4f7f\u7528\u76f8\u540c\u7684\u76f8\u5bf9\u9891\u7387\u516c\u5f0f\u8ba1\u7b97\u7684\uff0c\u5c3d\u7ba1\u4ece\u6982\u5ff5\u4e0a\u8bb2\u5b83\u4eec\u610f\u5473\u7740\u4e0d\u540c\u7684\u4e1c\u897f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-probabilidad-frecuencial\"><\/span>\u9891\u7387\u6982\u7387\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7ec3\u4e60\u6765\u8ba1\u7b97\u9891\u7387\u6982\u7387\u3002\u65e0\u8bba\u5982\u4f55\uff0c\u7531\u4e8e\u9891\u7387\u6982\u7387\u7684\u542b\u4e49\u4e0d\u592a\u5bb9\u6613\u7406\u89e3\uff0c\u5982\u679c\u60a8\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u53ef\u4ee5\u5728\u4e0b\u9762\u7684\u8bc4\u8bba\u4e2d\u7559\u4e0b\u3002<\/p>\n<ul>\n<li>\u8ba1\u7b97\u6784\u6210\u63b7\u9ab0\u5b50\u968f\u673a\u4f53\u9a8c\u7684\u57fa\u672c\u4e8b\u4ef6\u7684\u9891\u7387\u6982\u7387\u3002<\/li>\n<\/ul>\n<p>\u63b7\u9ab0\u5b50\u65f6\u6709\u516d\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\uff081\u30012\u30013\u30014\u30015 \u548c 6\uff09\uff0c\u56e0\u6b64\u6bcf\u4e2a\u57fa\u672c\u4e8b\u4ef6\u7684\u7406\u8bba\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-d8d6889656fa0d5faf24bf66b58d9e27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=\\cfrac{1}{6}=0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u591a\u6b21\u6a21\u62df\u53d1\u5c04\u5e76\u5c06\u7ed3\u679c\u8bb0\u5f55\u5728\u9891\u7387\u8868\u4e2d\u3002\u4f8b\u5982\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528 Excel \u8f6f\u4ef6\u3002<\/p>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u770b\u5230\u8fdb\u884c\u7684\u5b9e\u9a8c\u6570\u91cf\u7684\u91cd\u8981\u6027\uff0c\u6211\u4eec\u5c06\u9996\u5148\u6a21\u62df\u5341\u6b21\u53d1\u5c04\uff0c\u7136\u540e\u662f\u4e00\u767e\u6b21\uff0c\u6700\u540e\u662f\u4e00\u5343\u6b21\u3002\u56e0\u6b64\uff0c\u6a21\u62df 10 \u6b21\u968f\u673a\u63b7\u9ab0\u5b50\u5f97\u5230\u7684\u7ed3\u679c\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\/exemple-de-probabilite-de-frequence.png\" alt=\"\u9891\u7387\u6982\u7387\u793a\u4f8b\" class=\"wp-image-568\" width=\"502\" height=\"196\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u4ec5\u6a21\u62df\u5341\u6b21\u6295\u63b7\u6240\u83b7\u5f97\u7684\u9891\u7387\u6982\u7387\u4e0e\u7406\u8bba\u6982\u7387\u5e76\u4e0d\u76f8\u4f3c\u3002<\/p>\n<p>\u4f46\u968f\u7740\u6211\u4eec\u589e\u52a0\u5b9e\u9a8c\u6b21\u6570\uff0c\u8fd9\u4e24\u4e2a\u6307\u6807\u53d8\u5f97\u66f4\u52a0\u76f8\u4f3c\uff0c\u770b\u770b 100 \u6b21\u542f\u52a8\u7684\u6a21\u62df\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\/exemple-de-probabilite-frequentiste.png\" alt=\"\u9891\u7387\u6982\u7387\u7684\u4f8b\u5b50\" class=\"wp-image-570\" width=\"502\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u73b0\u5728\uff0c\u4e3a\u9ab0\u5b50\u4e0a\u7684\u6bcf\u4e2a\u6570\u5b57\u8ba1\u7b97\u7684\u9891\u7387\u6982\u7387\u4e0e\u5176\u7406\u8bba\u6982\u7387\u66f4\u52a0\u76f8\u4f3c\uff0c\u4f46\u662f\uff0c\u6211\u4eec\u4ecd\u7136\u5f97\u5230\u975e\u5e38\u4e0d\u540c\u7684\u503c\u3002<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u6267\u884c\u76f8\u540c\u7684\u8fc7\u7a0b\uff0c\u4f46\u6a21\u62df 1000 \u6b21\u542f\u52a8\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\/exercice-probabilite-resolu-frequent.png\" alt=\"\u9891\u7387\u6982\u7387\u7ec3\u4e60\u5df2\u89e3\u51b3\" class=\"wp-image-572\" width=\"503\" height=\"191\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u6700\u540e\u4e00\u4e2a\u8868\u4e2d\u770b\u5230\u7684\uff0c\u73b0\u5728\u9891\u7387\u6982\u7387\u7684\u503c\u975e\u5e38\u63a5\u8fd1\u7406\u8bba\u6982\u7387\u3002<\/p>\n<p>\u7efc\u4e0a\u6240\u8ff0\uff0c<strong>\u6211\u4eec\u8fdb\u884c\u7684\u5b9e\u9a8c\u6b21\u6570\u8d8a\u591a\uff0c\u4e8b\u4ef6\u53d1\u751f\u7684\u9891\u7387\u6982\u7387\u503c\u5c31\u8d8a\u63a5\u8fd1\u5176\u7406\u8bba\u53d1\u751f\u6982\u7387<\/strong>\u3002\u8be5\u89c4\u5219\u88ab\u5b9a\u4e49\u4e3a<strong><a href=\"https:\/\/statorials.org\/cn\/\u5927\u6570\u5b9a\u5f8b\/\">\u5927\u6570\u5b9a\u5f8b<\/a><\/strong>\uff0c\u5373\u8fed\u4ee3\u6b21\u6570\u8d8a\u591a\uff0c\u5b9e\u9a8c\u503c\u8d8a\u63a5\u8fd1\u7406\u8bba\u503c\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u5982\u679c\u6bd4\u8f83\u4e09\u4e2a\u9891\u7387\u8868\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u9891\u7387\u6982\u7387\u4e0d\u662f\u786e\u5b9a\u7684\uff0c\u800c\u662f\u6839\u636e\u8fed\u4ee3\u6b21\u6570\u800c\u53d8\u5316\u3002\u56e0\u6b64\uff0c\u60a8\u5fc5\u987b\u77e5\u9053\u5982\u4f55\u89e3\u91ca\u6240\u83b7\u5f97\u7684\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-frecuencial-y-probabilidad-teorica\"><\/span>\u9891\u7387\u6982\u7387\u548c\u7406\u8bba\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u9891\u7387\u6982\u7387\u4e0e\u7406\u8bba\u6982\u7387\uff08\u6216\u7ecf\u5178\u6982\u7387\uff09\u4e4b\u95f4\u7684\u533a\u522b\u5728\u4e8e<\/strong>\uff0c\u9891\u7387\u6982\u7387\u662f\u4f7f\u7528\u5b9e\u9a8c\u7ed3\u679c\u8ba1\u7b97\u7684\uff0c\u800c\u7406\u8bba\u6982\u7387\u662f\u8003\u8651\u7406\u60f3\u6761\u4ef6\u4e0b\u7684\u7ed3\u679c\u8ba1\u7b97\u7684\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e3a\u4e86\u627e\u5230\u9891\u7387\u6982\u7387\uff0c\u5fc5\u987b\u6a21\u62df\u5b9e\u9a8c\u5e76\u6839\u636e\u83b7\u5f97\u7684\u7ed3\u679c\u8fdb\u884c\u8ba1\u7b97\u3002\u4f46\u8981\u77e5\u9053\u7406\u8bba\u6982\u7387\uff0c\u4e0d\u5e94\u8be5\u8fdb\u884c\u5b9e\u9a8c\uff0c\u800c\u662f\u8fdb\u884c\u7406\u8bba\u8ba1\u7b97\u3002<\/p>\n<p>\u9891\u7387\u6982\u7387\u516c\u5f0f\u662f\u5b9e\u9a8c\u4e2d\u83b7\u5f97\u7684\u6709\u5229\u6848\u4f8b\u6570\u9664\u4ee5\u5c1d\u8bd5\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-d10bd148b769bd5e3c509ce78aaddb7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P_f=\\cfrac{\\text{n\\'umero de casos favorables en el experimento}}{\\text{n\\'umero total de intentos}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"400\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u76f8\u53cd\uff0c\u7406\u8bba\u6982\u7387\u516c\u5f0f\u662f\u6709\u5229\u4e8b\u4ef6\u7684\u6570\u91cf\u9664\u4ee5\u53ef\u80fd\u7684\u57fa\u672c\u4e8b\u4ef6\u7684\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-c18f28689a1a137a6c9c52ff5b64ddf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P_t=\\cfrac{\\text{n\\'umero de eventos favorables}}{\\text{n\\'umero total de eventos elementales}}\" title=\"Rendered by 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