{"id":26511,"date":"2021-03-29T13:00:19","date_gmt":"2021-03-29T13:00:19","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26511"},"modified":"2024-05-21T09:43:27","modified_gmt":"2024-05-21T09:43:27","slug":"%e6%a6%82%e7%8e%87%e8%ae%a1%e7%ae%97%e7%9a%84%e6%9c%89%e7%94%a8%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e6%a6%82%e7%8e%87%e8%ae%a1%e7%ae%97%e7%9a%84%e6%9c%89%e7%94%a8%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u6982\u7387\u8ba1\u7b97\u7684\u6709\u7528\u5b9a\u7406"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6982\u7387\u8ba1\u7b97\u7684\u6709\u7528\u5b9a\u7406<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u4e00\u4e9b\u7528\u4e8e\u6982\u7387\u8ba1\u7b97\u7684\u6709\u7528\u5b9a\u7406\u7684\u89e3\u7b54\u7ec3\u4e60\uff0c\u5305\u62ec\u8bc1\u660e\u548c\u63a8\u5bfc\u3002\u8fd9\u4e9b\u7ec3\u4e60\u6d89\u53ca\u8865\u6982\u7387\u3001\u96c6\u5408\u7684\u5305\u542b\u4ee5\u53ca\u4e8b\u4ef6\u7684\u6536\u655b\u3002\u5b8c\u6210\u8fd9\u4e9b\u7ec3\u4e60\u5c06\u4e3a\u6df1\u5165\u5b66\u4e60\u6982\u7387\u7406\u8bba\u63d0\u4f9b\u575a\u5b9e\u7684\u57fa\u7840\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u8fd9\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u8bc1\u660e<\/strong>\u6982\u7387\u7684\u57fa\u672c\u6027\u8d28<\/li>\n<\/ol>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/SSkPFP5FpKM\" title=\"YouTube \u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u770b\u5230\u7684\u662f\u4e00\u7cfb\u5217\u7ec3\u4e60\u6307\u5357\uff08\u5df2\u89e3\u51b3\uff09\uff0c\u5176\u76ee\u6807\u662f\u8bc1\u660e\u4e00\u4e9b\u5bf9\u6982\u7387\u7406\u8bba\u6709\u7528\u7684\u5b9a\u7406\u3002\u5c1d\u8bd5\u81ea\u5df1\u89e3\u51b3\u8fd9\u4e9b\u7ec3\u4e60\uff0c\u7136\u540e\u5bf9\u6bd4\u4f60\u7684\u7ed3\u679c &gt;:D<\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=111s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u8bc1\u660e <span class=\"katex-eq\" data-katex-display=\"false\">P(A^c) = 1 -P(A)<\/span>\uff0c\u5e76\u4e14\uff0c\u4ece\u6b64\u63a8\u5bfc\u51fa <span class=\"katex-eq\" data-katex-display=\"false\">P(\\emptyset) = 0<\/span><\/span><\/a><\/strong><br \/>\n<span class=\"collapseomatic \" id=\"id6a14a46d8007a\"  tabindex=\"0\" title=\"\u663e\u793a\u89e3\u51b3\u65b9\u6848\"    >\u663e\u793a\u89e3\u51b3\u65b9\u6848<\/span><div id=\"target-id6a14a46d8007a\" class=\"collapseomatic_content \">\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e<a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-medida-de-probabilidad\/\" target=\"_blank\" rel=\"noopener\">\u6982\u7387\u6d4b\u5ea6<\/a>\u7684\u5b9a\u4e49\uff0c\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u662f\u4efb\u4f55\u53ef\u6d4b\u4e8b\u4ef6\uff0c\u5219\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td>[a]<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">0\\leq P(A) \\leq 1<\/span><\/td>\n<\/tr>\n<tr>\n<td>[b]<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\cap B = \\emptyset \\rightarrow P(A\\cup B) = P(A) + P(B)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(\\Omega) = 1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u7531\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">A\\cap A^c = \\emptyset<\/span>\uff0c\u6839\u636e\u90e8\u5206 [b]\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td>[d]<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\cap A^c = \\emptyset \\rightarrow P(A\\cup A^c) = P(A) + P(A^c)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">A\\cap A^c = \\emptyset<\/span> \u603b\u662f\u6210\u7acb\uff0c\u5e76\u4e14 <span class=\"katex-eq\" data-katex-display=\"false\">A\\cup A^c = \\Omega<\/span>\uff0c\u6240\u4ee5\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">1=P(\\Omega) = P(A\\cup A^c) = P(A) + P(A^c)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A^c) = 1-P(A)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u5c31\u662f\u6211\u4eec\u8981\u8bc1\u660e\u7684\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4e3a\u4e86\u8bc1\u660e <span class=\"katex-eq\" data-katex-display=\"false\">P(\\emptyset)=0<\/span>\uff0c\u53ea\u9700\u5728\u521a\u521a\u8bc1\u660e\u7684\u5173\u7cfb\u4e2d\u53d6 <span class=\"katex-eq\" data-katex-display=\"false\">A = \\Omega<\/span>\uff0c\u6211\u4eec\u5c31\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(\\emptyset) = P(\\Omega^c) =1 - P(\\Omega) = 1-1 = 0<\/span>\n<\/div><\/li>\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=534s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">a) \u8bc1\u660e <span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B \\rightarrow P(B\\setminus A) = P(B) - P(A)<\/span><\/span><\/a>\uff0c\u8be5\u7b49\u5f0f\u4e00\u822c\u6210\u7acb\u5417\uff1f<\/strong><strong>b) \u8bc1\u660e <span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B \\rightarrow P(B)\\leq P(A)<\/span><\/strong><span class=\"collapseomatic \" id=\"id6a14a46d803c9\"  tabindex=\"0\" title=\"\u663e\u793a\u89e3\u51b3\u65b9\u6848 a)\"    >\u663e\u793a\u89e3\u51b3\u65b9\u6848 a)<\/span><div id=\"target-id6a14a46d803c9\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B<\/span>\uff1b \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv A\\cap B = A<\/span><\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">B\\setminus A = B\\cap A^c<\/span>\uff1b \u96c6\u5408\u8bba\u5b9a\u4e49<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">B= (B\\cap A) \\cup (B\\cap A^c)<\/span>\uff1b \u96c6\u5408\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(B\\cap A)\\cap (B\\cap A^c)=\\emptyset<\/span>\uff1b \u96c6\u5408\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B)= P[(B\\cap A) \\cup (B\\cap A^c)]<\/span>\uff1b \u6839\u636e(3)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B)= P (B\\cap A) + P(B\\cap A^c)<\/span>\uff1b \u6839\u636e(4) + \u6982\u7387\u6d4b\u5ea6\u5b9a\u4e49<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B)= P (B\\cap A) + P(B\\setminus A)<\/span>\uff1b \u6839\u636e(2)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> P(B\\setminus A) =P(B) - P (B\\cap A) <\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{P(B\\setminus A) =P(B) - P (A) }<\/span>\uff1b \u6839\u636e(1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\">{\\{A\\subseteq B\\}\\vdash P(B\\setminus A) = P(B) - P(A)}.<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8bf7\u6ce8\u610f\uff0c\u8fd9\u4e2a\u7b49\u5f0f\u4e0d\u662f\u4e00\u822c\u6210\u7acb\u7684\uff0c\u56e0\u4e3a\u5b83\u53d6\u51b3\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B<\/span> \u7684\u6210\u7acb\u3002\u6839\u636e\u8fd9\u4e9b\u63a8\u5bfc\uff0c\u53ef\u4ee5\u770b\u51fa\uff0c\u5982\u679c\u8fd9\u79cd\u60c5\u51b5\u4e0d\u6210\u7acb\uff0c\u5219 <span class=\"katex-eq\" data-katex-display=\"false\">P(B\\setminus A) = P(B) - P(A\\cap B).<\/span>\n<\/div>\n<span class=\"collapseomatic \" id=\"id6a14a46d8055a\"  tabindex=\"0\" title=\"\u663e\u793a\u89e3\u51b3\u65b9\u6848 b)\"    >\u663e\u793a\u89e3\u51b3\u65b9\u6848 b)<\/span><div id=\"target-id6a14a46d8055a\" class=\"collapseomatic_content \">\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e a) \u7684\u63a8\u7406\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\{A\\subseteq B\\}\\vdash P(B\\setminus A) = P(B) - P(A)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv \\{A\\subseteq B\\}\\vdash P(A) + P(B\\setminus A) = P(B)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u7531\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u662f\u6982\u7387\u6d4b\u5ea6\uff0c\u6240\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">\\forall X (P(X)\\geq 0),<\/span> \u56e0\u6b64\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">{\\{A\\subseteq B\\}\\vdash P(A) \\leq P(B)}.<\/span>\n<\/div>\n<p>&nbsp;<\/li>\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=892s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">a) \u8bc1\u660e <span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A) + P(B) - P(A\\cup B).<\/span><\/span><\/a> \u8bf7\u9644\u4e0a\u8bc1\u660e\u7684\u56fe\u793a\u3002<\/strong><strong>b) \u4f7f\u7528\u524d\u9762\u7684\u7ed3\u679c\u8bc1\u660e <span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) \\leq P(A) + P(B)<\/span><\/strong><span class=\"collapseomatic \" id=\"id6a14a46d80665\"  tabindex=\"0\" title=\"\u663e\u793a\u89e3\u51b3\u65b9\u6848 a)\"    >\u663e\u793a\u89e3\u51b3\u65b9\u6848 a)<\/span><div id=\"target-id6a14a46d80665\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\cup B = (A\\triangle B) \\cup (A\\cap B)<\/span>\uff1b \u96c6\u5408\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\triangle B := (A\\setminus B) \\cup (B\\setminus A)<\/span>\uff1b \u5bf9\u79f0\u5dee\u5b9a\u4e49<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(A\\triangle B)\\cap ( A \\cap B) = \\emptyset<\/span>\uff1b \u96c6\u5408\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(A\\setminus B)\\cap (B\\setminus A) = \\emptyset<\/span>\uff1b \u96c6\u5408\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P[(A\\triangle B) \\cup (A\\cap B)]<\/span>\uff1b \u6839\u636e(1)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A\\triangle B) + P(A\\cap B)]<\/span>\uff1b \u6839\u636e(3)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A\\setminus B) + P(B\\setminus A) + P(A\\cap B)]<\/span>\uff1b \u6839\u636e(2,4)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B\\setminus A) = P(B) - P(A\\cap B)<\/span>\uff1b \u5e94\u7528\u7ec3\u4e602\u7684\u7ed3\u679c<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(7)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\setminus B) = P(A) - P(A\\cap B)<\/span>\uff1b \u540c(6)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(8)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A) - P(A\\cap B) + P(B) - P(A\\cap B) + P(A\\cap B)<\/span>\uff1b \u6839\u636e(5,6,7)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{P(A\\cup B) = P(A) + P(B) - P(A\\cap B)}. <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<span class=\"collapseomatic \" id=\"id6a14a46d80842\"  tabindex=\"0\" title=\"\u663e\u793a\u89e3\u51b3\u65b9\u6848 b)\"    >\u663e\u793a\u89e3\u51b3\u65b9\u6848 b)<\/span><div id=\"target-id6a14a46d80842\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash P(A\\cup B) = P(A) + P(B) - P(A\\cap B)<\/span>\uff1b \u6839\u636ea)\u7684\u7ed3\u679c<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv\\; \\vdash P(A\\cup B) + P(A\\cap B) = P(A) + P(B) <\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv\\; \\vdash {P(A\\cup B) \\leq P(A) + P(B)} <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/li>\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=1625s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">\\{E_n\\}<\/span> \u662f\u4e00\u4e2a\u65e0\u9650\u4e8b\u4ef6\u65cf<\/span> <\/a>\uff0c\u4f7f\u5f97 <span class=\"katex-eq\" data-katex-display=\"false\">E_1\\supseteq E_2 \\supseteq E_3 \\supseteq \\cdots \\supseteq E_n \\supseteq E_{n+1}\\supseteq \\cdots.<\/span> \u8bc1\u660e\u5982\u4e0b\u547d\u9898\uff1a<\/strong>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = \\lim_{n\\to \\infty}P(E_n)<\/span>\n<span class=\"collapseomatic \" id=\"id6a14a46d80941\"  tabindex=\"0\" title=\"\u663e\u793a\u89e3\u51b3\u65b9\u6848\"    >\u663e\u793a\u89e3\u51b3\u65b9\u6848<\/span><div id=\"target-id6a14a46d80941\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">E_n \\supseteq E_{n+1}<\/span>\uff1b \u5047\u8bbe<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">E_n^c \\subseteq E_{n+1}^c<\/span>\uff1b \u6839\u636e(1)\u7684\u8865\u96c6<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle(E_n^c \\subseteq E_{n+1}^c) \\rightarrow P\\left( \\bigcup_{n=1}^\\infty E_n^c \\right)= \\lim_{n\\to\\infty}P(E_n^c)<\/span>\uff1b \u8fde\u7eed\u6027\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigcup_{n=1}^\\infty E_n^c = \\left( \\bigcap_{n=1}^\\infty E_n \\right)^c<\/span>\uff1b \u5fb7\u6469\u6839\u5f8b<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P\\left(E_n^c\\right) = 1 - P(E_n)<\/span>\uff1b \u5728\u7ec3\u4e601\u4e2d\u8bc1\u660e<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P\\left(\\left[ \\bigcap_{n=1}^\\infty E_n\\right]^c \\right) = \\lim_{n\\to\\infty}[1-P(E_n)] = 1 - \\lim_{n\\to\\infty}P(E_n)<\/span>\uff1b \u6839\u636e(2,4,5)\u5e94\u7528\u4e8e(3)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 1 - P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = 1 - \\lim_{n\\to\\infty}P(E_n) <\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{\\displaystyle P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = \\lim_{n\\to\\infty}P(E_n)} <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\therefore\\{E_n \\supseteq E_{n+1}\\}\\vdash P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = \\lim_{n\\to\\infty}P(E_n).<\/span>\n<p>&nbsp;<\/li>\n<\/ol>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u89e3\u51b3\u8fd9\u4e9b\u7ec3\u4e60\uff0c\u4f60\u5c06\u5b8c\u6210\u4e00\u4e2a\u652f\u67f1\uff0c\u4e3a\u7ee7\u7eed\u5b66\u4e60\u6982\u7387\u7406\u8bba\u63d0\u4f9b\u652f\u6301\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6982\u7387\u8ba1\u7b97\u7684\u6709\u7528\u5b9a\u7406 \u6458\u8981\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u4e00\u4e9b\u7528\u4e8e\u6982\u7387\u8ba1\u7b97\u7684\u6709\u7528\u5b9a\u7406\u7684\u89e3\u7b54\u7ec3\u4e60\uff0c\u5305\u62ec\u8bc1\u660e\u548c\u63a8\u5bfc\u3002\u8fd9\u4e9b\u7ec3\u4e60\u6d89\u53ca\u8865\u6982\u7387\u3001\u96c6\u5408\u7684\u5305\u542b\u4ee5\u53ca\u4e8b\u4ef6\u7684\u6536\u655b\u3002\u5b8c\u6210\u8fd9\u4e9b\u7ec3\u4e60\u5c06\u4e3a\u6df1\u5165\u5b66\u4e60\u6982\u7387\u7406\u8bba\u63d0\u4f9b\u575a\u5b9e\u7684\u57fa\u7840\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u8fd9\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u8bc1\u660e\u6982\u7387\u7684\u57fa\u672c\u6027\u8d28 \u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u770b\u5230\u7684\u662f\u4e00\u7cfb\u5217\u7ec3\u4e60\u6307\u5357\uff08\u5df2\u89e3\u51b3\uff09\uff0c\u5176\u76ee\u6807\u662f\u8bc1\u660e\u4e00\u4e9b\u5bf9\u6982\u7387\u7406\u8bba\u6709\u7528\u7684\u5b9a\u7406\u3002\u5c1d\u8bd5\u81ea\u5df1\u89e3\u51b3\u8fd9\u4e9b\u7ec3\u4e60\uff0c\u7136\u540e\u5bf9\u6bd4\u4f60\u7684\u7ed3\u679c &gt;:D \u8bc1\u660e \uff0c\u5e76\u4e14\uff0c\u4ece\u6b64\u63a8\u5bfc\u51fa a) \u8bc1\u660e \uff0c\u8be5\u7b49\u5f0f\u4e00\u822c\u6210\u7acb\u5417\uff1fb) \u8bc1\u660e &nbsp; a) \u8bc1\u660e \u8bf7\u9644\u4e0a\u8bc1\u660e\u7684\u56fe\u793a\u3002b) \u4f7f\u7528\u524d\u9762\u7684\u7ed3\u679c\u8bc1\u660e &nbsp; \u5982\u679c \u662f\u4e00\u4e2a\u65e0\u9650\u4e8b\u4ef6\u65cf \uff0c\u4f7f\u5f97 \u8bc1\u660e\u5982\u4e0b\u547d\u9898\uff1a \u901a\u8fc7\u89e3\u51b3\u8fd9\u4e9b\u7ec3\u4e60\uff0c\u4f60\u5c06\u5b8c\u6210\u4e00\u4e2a\u652f\u67f1\uff0c\u4e3a\u7ee7\u7eed\u5b66\u4e60\u6982\u7387\u7406\u8bba\u63d0\u4f9b\u652f\u6301\u3002<\/p>\n","protected":false},"author":1,"featured_media":26394,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[575,674],"tags":[],"class_list":["post-26511","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-575","category-674"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u6982\u7387\u8ba1\u7b97\u7684\u6709\u7528\u5b9a\u7406 - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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