{"id":50163,"date":"2024-06-11T20:15:47","date_gmt":"2024-06-11T20:15:47","guid":{"rendered":"https:\/\/science-hub.click\/%E5%A4%A7%E6%95%B0%E3%81%AE%E6%B3%95%E5%89%87%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":"2024-06-11T20:15:47","modified_gmt":"2024-06-11T20:15:47","slug":"%E5%A4%A7%E6%95%B0%E3%81%AE%E6%B3%95%E5%89%87%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=50163","title":{"rendered":"\u5927\u6570\u306e\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u5927\u6570\u306e\u6cd5\u5247\u306f<\/strong>\u3001 17<\/span>\u4e16\u7d00<\/sup>\u306b\u65b0\u3057\u3044\u6570\u5b66\u8a00\u8a9e\u304c\u767a\u898b\u3055\u308c\u305f\u969b\u306b\u5f62\u5f0f\u5316\u3055\u308c\u307e\u3057\u305f\u3002<\/p>

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\u307b\u3068\u3093\u3069\u306e\u4e16\u8ad6\u8abf\u67fb\u306f\u3053\u306e\u6cd5\u5f8b\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059[<\/span> 1 ]<\/span><\/sup> \u3002\u5f7c\u3089\u306f\u3001\u4eba\u53e3\u5168\u4f53\u306e\uff08\u304a\u305d\u3089\u304f\uff09\u610f\u898b\u3092\u77e5\u308b\u305f\u3081\u306b\u5341\u5206\u306a\u6570<\/a><\/span>\u306e\u4eba\u3005\u3092\u8abf\u67fb\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u5927\u6570\u306e\u6cd5\u5247<\/a><\/span>\u304c\u6b63\u5f0f\u306b\u78ba\u7acb\u3055\u308c\u306a\u3051\u308c\u3070\u3001\u4fdd\u967a\u304c\u3053\u308c\u307b\u3069\u6210\u9577\u3059\u308b\u3053\u3068\u306f\u3042\u308a\u3048\u307e\u305b\u3093\u3067\u3057\u305f\u3002\u5b9f\u969b\u3001\u3053\u306e\u6cd5\u5f8b\u306b\u3088\u308a\u3001\u4fdd\u967a\u4f1a\u793e\u306f\u3001\u8cac\u4efb\u3092\u8ca0\u3046\u640d\u5931\u304c\u767a\u751f\u3059\u308b\u304b\u3069\u3046\u304b\u306e\u78ba\u7387\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>

\u5927\u6570\u306e\u6cd5\u5247\u306f\u3001\u4e00\u9023\u306e\u5b9f\u9a13\u304b\u3089\u78ba\u7387\u6cd5\u5247\u3092<\/a><\/span>\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u63a8\u8ad6\u7d71\u8a08<\/span>\u3067\u3082\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>

\u6570\u5b66\u8005\u306f 2 \u3064\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3092\u533a\u5225\u3057\u3001\u305d\u308c\u305e\u308c\u300c\u5927\u6570\u306e\u5f31\u3044\u6cd5\u5247\u300d<\/strong><\/i>\u3068\u300c\u5927\u6570\u306e\u5f37\u3044\u6cd5\u5247\u300d<\/strong><\/i>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>

\u8208\u5473\u6df1\u3044\u306e\u306f\u3001\u5927\u6570\u306e\u6cd5\u5247\u304c\u5f62\u800c\u4e0a\u5b66\u7684\u306a\u7591\u554f\u3092\u63d0\u8d77\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u500b\u5225\u306b\u8003\u3048\u3089\u308c\u308b\u51fa\u6765\u4e8b\u304c\u5076\u7136\u306e\u5f71\u97ff<\/a><\/span><\/strong>\u3092\u53d7\u3051\u308b\u3053\u3068\u306b\u8ab0\u3082\u9a5a\u304b\u306a\u3044\u306e\u3067\u3059 (\u30b3\u30a4\u30f3\u3092 1000 \u56de\u8ee2\u304c\u3057\u3066 1000 \u56de\u306e\u88cf\u3092\u51fa\u3059\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3067\u306f\u3042\u308a\u307e\u305b\u3093…)\u3002\u305d\u308c\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u5b9f\u9a13\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u3042\u305f\u304b\u3082\u81ea\u7136\u306e\u30d0\u30e9\u30f3\u30b9\u6cd5\u5247\u304c\u5b58\u5728\u3059\u308b\u304b\u306e\u3088\u3046\u306b\u3001\u3042\u305f\u304b\u3082\u30ab\u30aa\u30b9\u306f\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u304b\u306e\u3088\u3046\u306b\u3001\u5168\u4f53\u7684\u306a<\/strong>\u53ef\u80fd\u6027\u306f\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059 (\u304a\u3088\u305d 50% \u306e\u8868\u3068 50% \u306e\u88cf\u304c\u5f97\u3089\u308c\u307e\u3059…)\u3002\u707d\u5bb3\u306a\u3093\u3066\u3042\u308a\u3048\u306a\u3044\u2026<\/p>

\u305f\u3060\u3057\u3001\u5e73\u5747<\/a><\/span>\u30b2\u30a4\u30f3\u3092\u7d76\u5bfe\u30b2\u30a4\u30f3\u3068\u6df7\u540c\u3057\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002 2 \u4eba\u306e\u30d7\u30ec\u30fc\u30e4\u30fc\u304c\u975e\u5e38\u306b\u9577\u3044\u9593\u8868\u304b\u88cf\u3067\u30d7\u30ec\u30fc\u3057\u3001\u8ca0\u3051\u305f\u30d7\u30ec\u30fc\u30e4\u30fc\u304c\u52dd\u3063\u305f\u30d7\u30ec\u30fc\u30e4\u30fc\u306b\u30e6\u30fc\u30ed\u3092\u4e0e\u3048\u308b\u5834\u5408\u3001\u5404\u30d7\u30ec\u30fc\u30e4\u30fc\u306e\u5e73\u5747\u8cde\u91d1\u306f\u4e8b\u5b9f\u4e0a 0 \u306b\u8fd1\u3065\u304f\u50be\u5411\u304c\u3042\u308a\u307e\u3059 (\u5e73\u5747\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059: \u8cde\u91d1\u3092\u6570\u5b57\u3067\u5272\u3063\u305f\u3082\u306e)\u305f\u3060\u3057\u3001\u5404\u30d7\u30ec\u30a4\u30e4\u30fc\u306e\u30b2\u30a4\u30f3\u306f\u3001\u632f\u5e45<\/a><\/span>\u304c\u5897\u52a0\u3057\u306a\u304c\u3089\u4ea4\u4e92\u306b\u4e0a\u6607\u3068\u4e0b\u964d\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002<\/p>

  1. \u2191<\/span>\u30af\u30a9\u30fc\u30bf\u30eb\u30fc\u30eb\u3092\u7279\u306b\u4f7f\u7528\u3057\u306a\u3044\u4eba<\/li><\/ol><\/div>

    \u5927\u6570\u306e\u5f31\u3044\u6cd5\u5247<\/span><\/h2>

    \u5927\u6570\u306e\u5f31\u3044\u6cd5\u5247\u306f\u3001\u30d2\u30f3\u30c1\u30f3\u306e\u5b9a\u7406<\/span><\/strong>\u3068\u3082\u547c\u3070\u308c\u307e\u3059 (\u307b\u3068\u3093\u3069\u4f7f\u7528\u3055\u308c\u307e\u305b\u3093)\u3002<\/p>

    \u540c\u3058\u78ba\u7387<\/a><\/span>\u306e\u6cd5\u5247\u3001\u6709\u9650\u5206\u6563<\/a><\/span>\u306e\u6cd5\u5247\u306b\u5f93\u3044\u3001\u671f\u5f85\u5024\u304cE(X)<\/i>\u3067\u3042\u308bn \u500b<\/i>\u306e\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u3092\u8003\u616e<\/a><\/span>\u3059\u308b\u3068\u3001\u5927\u6570\u306e\u5f31\u3044\u6cd5\u5247<\/strong>\u306b\u3088\u308a\u3001\u53b3\u5bc6\u306b\u6b63\u306e\u5b9f\u6570\u03b5<\/span>\u306b\u5bfe\u3057\u3066\u3001\u7d4c\u9a13\u7684\u5e73\u5747\u304c

    $$ {Y_n = \\frac{X_1+X_2+…+X_n}{n}} $$<\/div>\u306f\u671f\u5f85\u5024\u304b\u3089\u03b5 \u3092<\/span>\u8d85\u3048\u3066\u9038\u8131\u3057\u3001 n<\/i>\u306e\u5024\u304c\u5927\u304d\u3044\u5834\u5408\u306f 0 \u306b\u5411\u304b\u3046\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>
    $$ {\\lim_{n \\to +\\infty} P\\left(\\left|\\frac{X_1+X_2+…+X_n}{n} -E(X)\\right| \\geq \\epsilon\\right) = 0} $$<\/div><\/dd><\/dl>

    \u3053\u308c\u306f\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u8a3c\u660e\u3055\u308c\u307e\u3059\u3002 <\/p>

    $$ {P(|Y – E(Y)|\\geq \\epsilon) \\leq \\frac{V(Y)}{\\epsilon^2}} $$<\/div><\/dd><\/dl>

    \u305d\u3057\u3066\u3001\u5909\u6570<\/a><\/span>\u306b\u6ce8\u76ee\u3057\u3066\u304f\u3060\u3055\u3044\u3002

    $$ {Y_n = \\frac{X_1+X_2+…+X_n}{n}} $$<\/div>\u671f\u5f85\u5024 E(X) \u3068\u5206\u6563\u306b\u5bfe\u3057\u3066\u3042\u308a\u307e\u3059
    $$ {\\frac{V(X)}{n}} $$<\/div>\u305d\u308c\u3067<\/p>
    $$ {P\\left(\\left|\\frac{X_1+X_2+…+X_n}{n} -E(X)\\right| \\geq \\epsilon\\right) \\leq \\frac{V(X)}{n\\epsilon^2}} $$<\/div><\/dd><\/dl>

    \u307e\u305f\u3001 Y<\/i> n \u306f<\/i><\/sub><\/span>\u78ba\u7387\u7684\u306bE(X)<\/i>\u306b\u53ce\u675f\u3059\u308b\u3068\u3082\u8a00\u3044\u307e\u3059\u3002<\/p>

    \n\"\u5927\u6570\u306e\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

    \u5f37\u529b\u306a\u5927\u6570\u306e\u6cd5\u5247<\/span><\/h2>

    \u540c\u3058\u78ba\u7387\u6cd5\u5247\u306b\u5f93\u3046\u3001\u7a4d\u5206\u53ef\u80fd\u306an<\/i>\u500b\u306e\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u3092\u8003\u3048\u307e\u3059 (\u3064\u307e\u308a\u3001

    $$ {E(|X|)<\\infty} $$<\/div> \uff09\u3002\u4e0a\u8a18\u306e\u8868\u8a18\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u5f37\u529b\u306a\u5927\u6570\u306e\u6cd5\u5247\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u6307\u5b9a\u3055\u308c\u307e\u3059\u3002
    $$ {Y_n\\,} $$<\/div> \u300c\u307b\u307c\u78ba\u5b9f\u306b<\/i>\u300d E(X)<\/i>\u306b\u53ce\u675f\u3057\u307e\u3059\u3002<\/p>

    \u3064\u307e\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

    $$ {P\\left(\\lim_{n \\to +\\infty} Y_n(\\omega) = E(X)\\right)=1} $$<\/div><\/dd><\/dl>
    \n\"\u5927\u6570\u306e\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

    \u78ba\u7387\u6cd5\u5247\u3078\u306e\u53ce\u675f<\/span><\/span><\/h2>

    \u540c\u3058\u5927\u6570\u306e\u6cd5\u5247\u306b\u3088\u308a\u3001\u30b5\u30f3\u30d7\u30eb\u6bcd\u96c6\u56e3\u306e\u5206\u5e03\u306f\u3001 n<\/i>\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u5834\u5408\u306eX<\/i>\u306e\u78ba\u7387\u6cd5\u5247\u306b\u3088\u3063\u3066\u8fd1\u4f3c\u3067\u304d\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>

    \u5024x<\/i> i<\/i><\/sub><\/span>\u306e\u5468\u6ce2\u6570<\/a><\/span>f<\/i> n<\/i><\/sub> ( i<\/i> )<\/span>\u304c\u78ba\u7387p<\/i> i<\/i><\/sub><\/span>\u306b\u53ce\u675f\u3059\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u306b\u306f\u3001 X<\/i> (\u03c9) = x<\/i> i<\/i><\/sub><\/span>\u306e\u5834\u5408\u306f\u5024 1 \u3092\u3068\u308a\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f\u5024 0 \u3092\u3068\u308b\u78ba\u7387\u5909\u6570<\/a><\/span>\u3092\u4f7f\u7528\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/p>

    \u3053\u306e\u78ba\u7387\u5909\u6570\u306b\u306f\u671f\u5f85\u5024p<\/i> i \u304c<\/i><\/sub><\/span>\u3042\u308a\u307e\u3059\u3002<\/p>

    \u5468\u6ce2\u6570f<\/i> n<\/i><\/sub> ( i<\/i> )<\/span>\u306f\u78ba\u7387\u7684\u306b\u3001\u307e\u305f\u307b\u307c\u78ba\u5b9f\u306bp<\/i> i<\/i><\/sub><\/span>\u306b\u5411\u304b\u3063\u3066\u53ce\u675f\u3057\u307e\u3059\u3002<\/p><\/div>

    \n\"\u5927\u6570\u306e\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

    \u53c2\u8003\u8cc7\u6599<\/h2>
    1. \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u2013 arabe<\/a><\/li>
    2. Llei de los grandes n\u00famberos \u2013 asturien<\/a><\/li>
    3. B\u00f6y\u00fck \u0259d\u0259dl\u0259r qanunu \u2013 azerba\u00efdjanais<\/a><\/li>
    4. \u0417\u0430\u043a\u043e\u043d \u0432\u044f\u043b\u0456\u043a\u0456\u0445 \u043b\u0456\u043a\u0430\u045e \u2013 bi\u00e9lorusse<\/a><\/li>
    5. \u0417\u0430\u043a\u043e\u043d \u0437\u0430 \u0433\u043e\u043b\u0435\u043c\u0438\u0442\u0435 \u0447\u0438\u0441\u043b\u0430 \u2013 bulgare<\/a><\/li>
    6. Llei dels grans nombres \u2013 catalan<\/a><\/li><\/ol><\/div>\n
      \n

      \n \u5927\u6570\u306e\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
      \n \n
      \n
      \n