{"id":7804,"date":"2024-08-06T17:29:54","date_gmt":"2024-08-06T17:29:54","guid":{"rendered":"https:\/\/science-hub.click\/%E7%A2%BA%E7%8E%87%E8%AB%96%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-08-06T17:29:54","modified_gmt":"2024-08-06T17:29:54","slug":"%E7%A2%BA%E7%8E%87%E8%AB%96%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=7804","title":{"rendered":"\u78ba\u7387\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"
\n\"\u78ba\u7387\u66f2\u7dda\u3002\"<\/figure>
\u78ba\u7387\u66f2\u7dda\u3002<\/div><\/div><\/div>

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\u6b74\u53f2\u7684<\/span><\/h2>

\u78ba\u7387\u306e\u6570\u5b66\u7406\u8ad6\u306f\u300116 \u4e16\u7d00\u306e\u30b8\u30a7\u30ed\u30e9\u30e2 \u30ab\u30eb\u30c0\u30fc\u30ce<\/a><\/span>\u3001\u304a\u3088\u3073 17 \u4e16\u7d00\u306e\u30d4\u30a8\u30fc\u30eb \u30c9 \u30d5\u30a7\u30eb\u30de\u30fc<\/a><\/span>\u3068\u30d6\u30ec\u30fc\u30ba \u30d1\u30b9\u30ab\u30eb<\/a><\/span>\u306b\u3088\u308b\u5076\u7136<\/a><\/span>\u306e\u30b2\u30fc\u30e0\u306e\u5206\u6790\u306b\u8d77\u6e90\u3092\u6301\u3061\u307e\u3059\u3002\u5358\u7d14\u306a\u30b3\u30a4\u30f3\u6295\u3052\u3084\u30b5\u30a4\u30b3\u30ed\u306e\u6295\u3052\u306f\u30e9\u30f3\u30c0\u30e0\u306a\u51fa\u6765\u4e8b\u3067\u3059\u304c\u3001\u305d\u308c\u3092\u4f55\u5ea6\u3082\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3067\u3001\u7279\u5b9a\u306e\u7d71\u8a08\u7684\u7279\u6027\u3092\u6301\u3064\u4e00\u9023\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u3001\u305d\u308c\u3092\u7814\u7a76\u3057\u3066\u4e88\u6e2c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u70b9\u306b\u95a2\u3059\u308b 2 \u3064\u306e\u57fa\u672c\u7684\u306a\u6570\u5b66\u7684\u7d50\u679c\u306f\u3001\u5927\u6570\u306e\u6cd5\u5247<\/a><\/span>\u3068\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406<\/a><\/span>\u3067\u3059\u3002<\/p>

\u5f53\u521d\u3001\u78ba\u7387\u7406\u8ad6\u306f\u4e3b\u306b\u96e2\u6563<\/strong>\u4e8b\u8c61\u3092\u8003\u616e\u3057\u3066\u304a\u308a\u3001\u305d\u306e\u624b\u6cd5\u306f\u4e3b\u306b\u7d44\u307f\u5408\u308f\u305b\u8ad6\u3067\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u5206\u6790\u7684\u8003\u5bdf\u306b\u3088\u308a\u3001\u7406\u8ad6\u306b\u9023\u7d9a<\/strong>\u78ba\u7387\u5909\u6570\u3092\u5c0e\u5165\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u8003\u3048\u65b9\u306f\u73fe\u4ee3\u306e\u78ba\u7387\u7406\u8ad6\u306b\u7aef<\/a><\/span>\u3092\u767a\u3057\u3066\u304a\u308a\u3001\u305d\u306e\u57fa\u790e<\/span>\u306f\u30a2\u30f3\u30c9\u30ec\u30a4\u30fb\u30cb\u30b3\u30e9\u30a8\u30f4\u30a3\u30c3\u30c1\u30fb\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u306b\u3088\u3063\u3066\u7bc9\u304b\u308c\u307e\u3057\u305f\u3002\u30b3\u30eb\u30e2\u30b4\u30ed\u30d5\u306f\u3001\u30ea\u30d2\u30e3\u30eb\u30c8\u30fb\u30d5\u30a9\u30f3\u30fb\u30df\u30fc\u30bc\u30b9<\/a><\/span>\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u305f\u5b87\u5b99<\/a><\/span>\u306e\u6982\u5ff5\u3068\u6e2c\u5b9a\u7406\u8ad6\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u30011933 \u5e74\u306b\u78ba\u7387\u8ad6\u306e\u516c\u7406\u7cfb\u3092\u767a\u8868\u3057\u307e\u3057\u305f\u3002\u3059\u3050\u306b\u3001\u5f7c\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u73fe\u4ee3\u306e\u78ba\u7387\u306e\u8b70\u8ad6\u306e\u4f59\u5730\u306e\u306a\u3044\u57fa\u790e\u3068\u306a\u308a\u307e\u3057\u305f\u3002<\/p>

\u96e2\u6563\u78ba\u7387\u7406\u8ad6<\/span><\/h3>

\u96e2\u6563\u78ba\u7387\u7406\u8ad6\u306f\u3001<\/strong>\u53ef\u7b97\u5b87\u5b99\u306e\u6587\u8108\u306b\u304a\u3051\u308b\u51fa\u6765\u4e8b\u3092\u6271\u3044\u307e\u3059\u3002<\/p>

\u4f8b: \u30b5\u30a4\u30b3\u30ed\u632f\u308a\u3001\u30ab\u30fc\u30c9\u30c7\u30c3\u30ad\u306e\u5b9f\u9a13\u3001\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30ad\u30f3\u30b0<\/a><\/span>\u3002<\/p>

\u53e4\u5178\u7684\u306a\u5b9a\u7fa9<\/a><\/span><\/strong>: \u5f53\u521d\u3001\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u306f<\/a><\/span>\u3001\u305d\u306e\u30a4\u30d9\u30f3\u30c8\u306b\u3068\u3063\u3066\u6709\u5229\u306a\u30b1\u30fc\u30b9\u306e\u6570\u3092\u3001\u30e9\u30f3\u30c0\u30e0\u5b9f\u9a13\u3067\u8003\u3048\u3089\u308c\u308b\u7d50\u679c\u306e\u7dcf\u6570<\/a><\/span>\u3067\u5272\u3063\u305f\u3082\u306e\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002<\/p>

\u305f\u3068\u3048\u3070\u3001\u30a4\u30d9\u30f3\u30c8\u304c\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u3066\u5076\u6570\u306e\u76ee\u304c\u51fa\u305f<\/i>\u5834\u5408\u3001\u305d\u306e\u78ba\u7387\u306f\u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u3089\u308c<\/span>\u307e\u3059\u3002

$$ {\\frac{3}{6}=\\frac{1}{2}} $$<\/div> , 6 \u3064\u306e\u9762\u306e\u3046\u3061 3 \u3064\u306e\u9762\u304c\u5076\u6570\u3067\u3042\u308b\u305f\u3081\u3067\u3059\u3002<\/p>

\u73fe\u4ee3\u306e\u5b9a\u7fa9<\/strong>: \u73fe\u4ee3\u306e\u5b9a\u7fa9\u306f\u3001\u53e4\u5178\u7684\u306a\u5b9a\u7fa9\u306b\u304a\u3051\u308b\u7d4c\u9a13\u306e\u53ef\u80fd\u306a\u7d50\u679c\u306e\u30bb\u30c3\u30c8\u306b\u5bfe\u5fdc\u3059\u308b\u3001\u5b87\u5b99\u3068\u547c\u3070\u308c\u308b\u30bb\u30c3\u30c8<\/a><\/span>\u304b\u3089\u59cb\u307e\u308a\u307e\u3059\u3002\u6ce8\u76ee\u3055\u308c\u308b

$$ {\\Omega=\\left \\{ x_1,x_2,\\dots\\right \\}} $$<\/div> \u3002\u6b21\u306b\u3001 \u03a9<\/span>\u306b\u5bfe\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570f \u304c<\/i><\/span>\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u306e\u78ba\u7387\u3092\u03a9<\/span>\u306e\u5404\u8981\u7d20\u306b\u95a2\u9023\u4ed8\u3051\u308b\u305f\u3081\u3001\u6b21\u306e\u7279\u6027\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 <\/p>
  1. $$ {f(x)\\in[0,1]\\mbox{ pour tout }x\\in \\Omega} $$<\/div><\/li>
  2. $$ {\\sum_{x\\in \\Omega} f(x) = 1} $$<\/div><\/li><\/ol>

    \u6b21\u306b\u3001\u30a4\u30d9\u30f3\u30c8\u3092\u7d50\u679c\u306e\u30bb\u30c3\u30c8\u3001\u3064\u307e\u308a\u03a9<\/span>\u306e\u30b5\u30d6\u30bb\u30c3\u30c8<\/a><\/span>\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u30a4\u30d9\u30f3\u30c8E<\/i><\/span>\u306e\u78ba\u7387\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u81ea\u7136\u306a\u65b9\u6cd5\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p>

    $$ {P(E)=\\sum_{x\\in E} f(x)\\,} $$<\/div><\/dd><\/dl>

    \u3057\u305f\u304c\u3063\u3066\u3001\u5b87\u5b99\u306e\u78ba\u7387\u306f 1 \u3067\u3001\u30cc\u30eb \u30a4\u30d9\u30f3\u30c8 (\u7a7a\u96c6\u5408) \u306e\u78ba\u7387\u306f 0 \u3067\u3059\u3002<\/p>

    \u30b5\u30a4\u30b3\u30ed\u3092\u632f\u308b\u4f8b\u306b\u623b\u308b\u3068\u3001\u30b5\u30a4\u30b3\u30ed\u306e\u53ef\u80fd\u306a\u5024\u306b\u5bfe\u5fdc\u3059\u308b\u5b87\u5b99\u03a9 = {1;2;3;4;5;6}<\/span>\u3068\u95a2\u6570f<\/i><\/span>\u3092\u4e0e\u3048\u308b\u3053\u3068\u3067\u3001\u3053\u306e\u7d4c\u9a13\u3092\u30e2\u30c7\u30eb\u5316\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u305e\u308c\u306b

    $$ {i\\in\\Omega} $$<\/div>\u30d1\u30fc\u30c8\u30ca\u30fc
    $$ {f(i)=\\frac{1}{6}} $$<\/div> \u3002<\/p>

    \u9023\u7d9a\u78ba\u7387\u7406\u8ad6<\/span><\/h3>

    \u9023\u7d9a\u78ba\u7387\u7406\u8ad6\u306f\u3001<\/strong>\u9023\u7d9a\u3057\u305f\u5b87\u5b99 (\u5b9f\u7dda\u306a\u3069) \u3067\u767a\u751f\u3059\u308b\u4e8b\u8c61\u3092\u6271\u3044\u307e\u3059\u3002<\/p>

    \u53e4\u5178\u7684\u5b9a\u7fa9<\/strong>: \u53e4\u5178\u7684\u5b9a\u7fa9\u306f\u3001\u9023\u7d9a\u4e8b\u4f8b\u306b\u76f4\u9762\u3059\u308b\u3068\u7121\u52b9\u306b\u306a\u308a\u307e\u3059 (\u30d9\u30eb\u30c8\u30e9\u30f3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9<\/a><\/span>\u3092\u53c2\u7167)\u3002<\/p>

    \u73fe\u4ee3\u306e\u5b9a\u7fa9<\/strong>\u5b87\u5b99\u304c\u5b9f\u7dda\u306a\u3089

    $$ {\\mathbb{R}} $$<\/div> \u3001\u6b21\u306b\u3001\u5206\u5e03\u95a2\u6570\u3068\u547c\u3070\u308c\u308b\u95a2\u6570\u306e\u5b58\u5728\u3092\u4eee\u5b9a\u3057\u307e\u3059\u3002
    $$ {F\\,} $$<\/div> \u3001\u305d\u308c\u306f\u4e0e\u3048\u308b
    $$ {P(X\\le x) = F(x)\\,} $$<\/div>\u78ba\u7387<\/i><\/span>\u5909\u6570\u306e\u5834\u5408\u3064\u307e\u308a\u3001 F<\/i> ( x<\/i> ) \u306f<\/span>\u3001 X \u304c<\/i><\/span>x<\/i><\/span>\u4ee5\u4e0b\u3067\u3042\u308b\u78ba\u7387\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>

    \u5206\u5e03\u95a2\u6570\u306f\u6b21\u306e\u7279\u6027\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>

    1. $$ {F\\,} $$<\/div>\u306f\u53f3\u9023\u7d9a\u5897\u52a0\u95a2\u6570\u3067\u3059\u3002 <\/li>
    2. $$ {\\lim_{x\\rightarrow -\\infty} F(x)=0} $$<\/div><\/li>
    3. $$ {\\lim_{x\\rightarrow \\infty} F(x)=1} $$<\/div><\/li><\/ol>

      \u3082\u3057

      $$ {F\\,} $$<\/div>\u304c\u5fae\u5206\u53ef\u80fd\u3067<\/a><\/span>\u3042\u308b\u5834\u5408\u3001\u78ba\u7387\u5909\u6570<\/i><\/span>\u306f
      $$ {f(x)=\\frac{dF(x)}{dx}\\,} $$<\/div> \u3002<\/p>

      \u30bb\u30c3\u30c8\u306e\u5834\u5408

      $$ {E \\subseteq \\mathbb{R}} $$<\/div> \u3001\u78ba\u7387<\/i><\/span>\u5909\u6570\u304c
      $$ {E\\,} $$<\/div>\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p>
      $$ {P(X\\in E) = \\int_{x\\in E} dF(x)\\,} $$<\/div><\/dd><\/dl>

      \u78ba\u7387\u5bc6\u5ea6<\/a><\/span>\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306f\u3001\u305d\u308c\u3092\u66f8\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

      $$ {P(X\\in E) = \\int_{x\\in E} f(x)\\,dx} $$<\/div><\/dd><\/dl>

      \u78ba\u7387\u5bc6\u5ea6\u306f\u9023\u7d9a\u78ba\u7387\u5909\u6570\u306b\u5bfe\u3057\u3066\u306e\u307f\u5b58\u5728\u3057\u307e\u3059\u304c\u3001\u5206\u5e03\u95a2\u6570\u306f\u5024\u304c\u6b21\u306e\u4efb\u610f\u306e\u78ba\u7387\u5909\u6570 (\u96e2\u6563\u5909\u6570\u3092\u542b\u3080) \u306b\u5bfe\u3057\u3066\u5b58\u5728\u3057\u307e\u3059\u3002

      $$ {\\mathbb{R}} $$<\/div> \u3002<\/p>

      \u3053\u308c\u3089\u306e\u6982\u5ff5\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u591a\u6b21\u5143\u306e\u5834\u5408\u306b\u4e00\u822c\u5316\u3067\u304d\u307e\u3059\u3002

      $$ {\\mathbb{R}^n} $$<\/div>\u304a\u3088\u3073\u4ed6\u306e\u9023\u7d9a\u5b87\u5b99\u3002<\/p>
      \n\"\u78ba\u7387\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

      \u4eca\u65e5\u306e\u78ba\u7387\u8ad6<\/span><\/h2>

      \u4e00\u90e8\u306e\u5206\u5e03\u306f\u96e2\u6563\u5206\u5e03<\/i>\u3068\u9023\u7d9a<\/i>\u5206\u5e03\u306e\u6df7\u5408<\/a><\/span>\u3067\u3042\u308b\u305f\u3081\u3001\u78ba\u7387\u5bc6\u5ea6\u3082\u8cea\u91cf<\/a><\/span>\u95a2\u6570\u3082\u6301\u305f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30ab\u30f3\u30c8\u30fc\u30eb\u5206\u5e03\u306f\u305d\u306e\u3088\u3046\u306a\u4f8b\u3067\u3059\u3002\u78ba\u7387\u306b\u5bfe\u3059\u308b\u6700\u65b0\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u306f\u3001\u6e2c\u5ea6\u7406\u8ad6\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u7a7a\u9593<\/a><\/span>\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u3001\u3053\u308c\u3089\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>

      \u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u308b\u3068

      $$ {\\Omega\\,} $$<\/div> \u03c3\u4ee3\u6570\u3092\u5099\u3048\u305f\u5b87\u5b99\uff08\u5b87\u5b99\u3068\u3082\u547c\u3070\u308c\u308b\uff09
      $$ {\\mathcal{F}\\,} $$<\/div> \u3001\u5bfe\u7b56
      $$ {\\mu\\,} $$<\/div>\u6b21\u306e\u5834\u5408\u3001 \u306f\u78ba\u7387\u6e2c\u5ea6<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002 <\/p>
      1. $$ {\\mu\\,} $$<\/div>\u524d\u5411\u304d\u306a\u63aa\u7f6e\u3067\u3059<\/li>
      2. $$ {\\mu(\\Omega)=1\\,} $$<\/div><\/li><\/ol>

        \u5404\u5206\u5e03\u95a2\u6570\u306b\u306f\u3001\u30dc\u30ec\u30ea\u30a2\u30f3\u4e0a\u306b\u56fa\u6709\u306e\u78ba\u7387\u5c3a\u5ea6\u304c\u5b58\u5728\u3057\u3001\u305d\u306e\u9006\u3082\u540c\u69d8\u3067\u3059\u3002\u5206\u5e03\u95a2\u6570\u306b\u5bfe\u5fdc\u3059\u308b\u6e2c\u5b9a\u306f\u3001\u305d\u306e\u95a2\u6570\u306b\u3088\u3063\u3066\u5f15\u304d\u8d77\u3053\u3055\u308c\u308b\u3068<\/strong>\u8a00\u308f\u308c\u307e\u3059\u3002\u9023\u7d9a\u306e\u5834\u5408\u3001\u3053\u306e\u6e2c\u5ea6\u306f\u3001f \u304c\u5206\u5e03\u95a2\u6570 (\u5fc5\u305a\u3057\u3082\u5b58\u5728\u3059\u308b\u5fc5\u8981\u306f\u306a\u3044) \u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u78ba\u7387\u5bc6\u5ea6\u3067\u3042\u308b\u5834\u5408\u3001\u30eb\u30d9\u30fc\u30b0\u6e2c\u5ea6\u306e<\/a><\/span>\u03bb<\/span>\u3092\u6301\u3064\u6e2c\u5ea6f<\/i> d<\/i> \u03bb<\/span>\u3068\u4e00\u81f4\u3057\u307e\u3059\u304c\u3001\u96e2\u6563\u306e\u5834\u5408\u3001\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 f \u3068\u4e00\u81f4\u3057\u307e\u3059\u3002\u4ee5\u524d\u3002<\/p>

        \u6e2c\u5ea6\u7406\u8ad6\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u3088\u308a\u3001\u78ba\u7387\u306e\u96e2\u6563\u7406\u8ad6\u3068\u9023\u7d9a\u7406\u8ad6\u3092\u3088\u308a\u3088\u304f\u7406\u89e3\u3057\u3066\u7d71\u4e00\u3067\u304d\u308b<\/a><\/span>\u3088\u3046\u306b\u306a\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u78ba\u7387\u306e\u7bc4\u56f2\u5916\u3067\u78ba\u7387\u306b\u3064\u3044\u3066\u8a71\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002

        $$ {\\mathbb{R}^n} $$<\/div> \u3001\u7279\u306b\u78ba\u7387\u904e\u7a0b\u306e\u7406\u8ad6\u306b\u304a\u3044\u3066\u3002\u305f\u3068\u3048\u3070\u3001\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\u306e\u7814\u7a76\u3067\u306f\u3001\u78ba\u7387\u306f\u95a2\u6570\u7a7a\u9593\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>

        \u78ba\u7387\u306e\u6cd5\u5247<\/span><\/h2>

        \u7279\u5b9a\u306e\u78ba\u7387\u5909\u6570\u306f\u591a\u304f\u306e\u81ea\u7136\u904e\u7a0b\u3067\u898b\u3089\u308c\u308b\u305f\u3081\u3001\u78ba\u7387\u8ad6\u3067\u983b\u7e41\u306b\u906d\u9047\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5f7c\u3089\u306e\u6cd5\u5247\u306f\u7279\u306b\u91cd\u8981\u3067\u3059\u3002\u6700\u3082\u4e00\u822c\u7684\u306a\u96e2\u6563\u6cd5\u5247\u306f\u3001\u96e2\u6563\u4e00\u69d8\u6cd5\u5247<\/a><\/span>\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u306e\u6cd5\u5247<\/a><\/span>\u3001\u304a\u3088\u3073\u4e8c\u9805\u6cd5\u5247\u3001\u30dd\u30a2\u30bd\u30f3\u6cd5\u5247<\/a><\/span>\u3001\u304a\u3088\u3073\u5e7e\u4f55\u5b66\u6cd5\u5247\u3067\u3059\u3002\u4e00\u69d8\u9023\u7d9a\u6cd5\u5247\u3001\u6b63\u898f\u6cd5\u5247\u3001\u6307\u6570\u95a2\u6570\u6cd5\u5247<\/a><\/span>\u3001\u304a\u3088\u3073\u30ac\u30f3\u30de\u6cd5\u5247\u306f\u3001\u6700\u3082\u91cd\u8981\u306a\u9023\u7d9a\u6cd5\u5247\u306e 1 \u3064\u3067\u3059\u3002<\/p>

        \u78ba\u7387\u5909\u6570\u306e\u53ce\u675f<\/a><\/span><\/span><\/h2>

        \u78ba\u7387\u7406\u8ad6\u3067\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u53ce\u675f<\/span>\u306b\u3064\u3044\u3066\u3044\u304f\u3064\u304b\u306e\u6982\u5ff5\u304c\u3042\u308a\u307e\u3059\u3002\u30ea\u30b9\u30c8\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>

        \u6cd5\u5247\u306e\u53ce\u675f<\/strong>: \u4e00\u9023\u306e\u78ba\u7387\u5909\u6570
        $$ {(X_n)_{n\\in\\mathbb{N}}} $$<\/div>\u78ba\u7387\u5909\u6570\u306b\u5411\u304b\u3063\u3066\u6cd5\u5247\u7684\u306b\u53ce\u675f\u3057\u307e\u3059
        $$ {X\\,} $$<\/div>\u4e00\u9023\u306e\u753b\u50cf\u6e2c\u5b9a\u304c\u884c\u308f\u308c\u308b\u5834\u5408\u306b\u9650\u308a\u3001
        $$ {(\\mu_{X_n})_n\\in\\mathbb{N}} $$<\/div>\u753b\u50cf\u6e2c\u5b9a\u5024\u03bc<\/i><\/sub><\/span>\u306b\u8fd1\u304f\u53ce\u675f\u3057\u307e\u3059\u7279\u306b\u5b9f\u969b\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u5206\u5e03\u95a2\u6570\u306f\u5358\u7d14\u306b X \u306e\u5206\u5e03\u95a2\u6570\u306b\u53ce\u675f\u3059\u308b<\/span>\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/dd>
        \u78ba\u7387\u306e\u53ce\u675f<\/strong>:
        $$ {(X_n)_{n\\in\\mathbb{N}}} $$<\/div>\u78ba\u7387\u7684\u306b\u306f\uff5e\u306b\u53ce\u675f\u3059\u308b
        $$ {X\\,} $$<\/div> ssi
        $$ {\\forall \\epsilon width=} $$<\/div> 0″ >\u3001
        $$ {\\lim_{n\\rightarrow\\infty}P\\left(\\left|X_n-X\\right|\\geq\\varepsilon\\right)=0} $$<\/div> \u3002\u3053\u306e\u53ce\u675f\u306f\u6cd5\u5f8b\u306e\u53ce\u675f\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/dd>
        \u307b\u307c\u78ba\u5b9f\u306b\u53ce\u675f\u3057\u307e\u3059<\/strong>:
        $$ {(X_n)_{n\\in\\mathbb{N}}} $$<\/div>\u307b\u307c\u78ba\u5b9f\u306b\u5411\u304b\u3063\u3066\u53ce\u675f\u3059\u308b
        $$ {X\\,} $$<\/div> ssi
        $$ {P(\\{\\omega\/\\lim_{n\\rightarrow\\infty} X_n(\\omega)=X(\\omega)\\})=1.} $$<\/div> \u3002\u305d\u308c\u306f\u78ba\u7387\u306e\u53ce\u675f\u3001\u3057\u305f\u304c\u3063\u3066\u6cd5\u5247\u306e\u53ce\u675f\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/dd>
        \u3067\u306e\u53ce\u675f<\/strong>$$ {\\mathcal{L}^1} $$<\/dd><\/dl><\/div> :
        $$ {(X_n)_{n\\in\\mathbb{N}}} $$<\/div>\u306b\u53ce\u675f\u3059\u308b
        $$ {\\mathcal{L}^1} $$<\/div>\u306b\u5411\u304b\u3063\u3066
        $$ {X\\,} $$<\/div> ssi
        $$ {\\lim_{n\\rightarrow\\infty}E(|X_n-X|)=0} $$<\/div> \u3002\u307e\u305f\u3001\u78ba\u7387\u306e\u53ce\u675f\u3082\u610f\u5473\u3057\u307e\u3059\u3002<\/div>\n
        \n \"\u78ba\u7387\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"\n<\/figure>\n

        \u53c2\u8003\u8cc7\u6599<\/h2>\n
        1. Waarskynlikheidsleer \u2013 afrikaans<\/a><\/li>
        2. \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 \u2013 arabe<\/a><\/li>
        3. Teor\u00eda de la probabilid\u00e1 \u2013 asturien<\/a><\/li>
        4. Ehtimal n\u0259z\u0259riyy\u0259si \u2013 azerba\u00efdjanais<\/a><\/li>
        5. \u0627\u06cc\u062d\u062a\u06cc\u0645\u0627\u0644 \u0646\u0638\u0631\u06cc\u0647\u200c\u0633\u06cc \u2013 South Azerbaijani<\/a><\/li>
        6. \u0418\u0445\u0442\u0438\u043c\u0430\u043b\u043b\u044b\u04a1 \u0442\u0435\u043e\u0440\u0438\u044f\u04bb\u044b \u2013 bachkir<\/a><\/li><\/ol>\n
          \n

          \n \u78ba\u7387\u8ad6\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
          \n \n
          \n
          \n