{"id":105085,"date":"2024-08-28T20:26:21","date_gmt":"2024-08-28T20:26:21","guid":{"rendered":"https:\/\/science-hub.click\/%E9%9B%A2%E6%95%A3%E7%B5%B1%E4%B8%80%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":"2024-08-28T20:26:21","modified_gmt":"2024-08-28T20:26:21","slug":"%E9%9B%A2%E6%95%A3%E7%B5%B1%E4%B8%80%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=105085","title":{"rendered":"\u96e2\u6563\u7d71\u4e00\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
\u96e2\u6563\u5747\u4e00\u6cd5\u5247<\/th><\/tr>
\n\"n=5<\/figure><\/td><\/tr>
\n\"n=5<\/figure><\/td><\/tr>
<\/td><\/tr>
\u8a2d\u5b9a<\/th>
$$ {a \\in (…,-2,-1,0,1,2,…)\\,} $$<\/div>
$$ {b \\in (…,-2,-1,0,1,2,…)\\,} $$<\/div>
$$ {n=b-a+1\\,} $$<\/div><\/td><\/tr>
\u30b5\u30dd\u30fc\u30c8<\/th>
$$ {k \\in \\{a,a+1,…,b-1,b\\}\\,} $$<\/div><\/td><\/tr>
\u78ba\u7387\u5bc6\u5ea6<\/a><\/span>(\u8cea\u91cf\u95a2\u6570) <\/th>
$$ { \\begin{matrix} \\frac{1}{n} & \\mbox{pour }a\\le k \\le b\\ \\\\0 & \\mbox{sinon } \\end{matrix} } $$<\/div><\/td><\/tr>
\u5206\u5e03\u95a2\u6570<\/a><\/span><\/th>
$$ { \\begin{matrix} 0 & \\mbox{pour }kb \\end{matrix} } $$<\/a\\\\><\/div><\/tr>
\u5e0c\u671b<\/th>
$$ {\\frac{a+b}{2}\\,} $$<\/div><\/td><\/tr>
\u4e2d\u592e\u5024<\/a><\/span>\uff08\u4e2d\u592e\uff09 <\/th>
$$ {a+n\/2\\,} $$<\/div><\/td><\/tr>
\u30d5\u30a1\u30c3\u30b7\u30e7\u30f3<\/th>\u8a72\u5f53\u306a\u3057<\/td><\/tr>
\u5206\u6563<\/a><\/span><\/th>
$$ {\\frac{n^2-1}{12}\\,} $$<\/div><\/td><\/tr>
\u975e\u5bfe\u79f0\u6027<\/a><\/span>\uff08\u7d71\u8a08\uff09 <\/th>
$$ {0\\,} $$<\/div><\/td><\/tr>
\u5c16\u5ea6(\u975e\u6a19\u6e96\u5316) <\/th>
$$ {\\frac{9(n^2+1)}{5(n^2-1)}\\,} $$<\/div><\/td><\/tr>
\u30a8\u30f3\u30c8\u30ed\u30d4<\/a><\/span><\/th>
$$ {\\ln(n)\\,} $$<\/div><\/td><\/tr>
\u30e2\u30fc\u30e1\u30f3\u30c8\u767a\u751f\u6a5f\u80fd<\/a><\/span><\/th>
$$ {\\frac{e^{at}}{n}\\sum_{k=0}^{n-1}e^{kt}\\,} $$<\/div><\/td><\/tr>
\u7279\u5fb4\u7684\u306a\u6a5f\u80fd<\/a><\/span><\/th>
$$ {\\frac{e^{iat}}{n}\\sum_{k=0}^{n-1}e^{ikt}\\,} $$<\/div><\/td><\/tr><\/table>

\u78ba\u7387\u7406\u8ad6<\/a><\/span>\u3067\u306f\u3001\u4e00\u69d8\u96e2\u6563\u6cd5\u5247<\/b>\u306f\u3001\u53ef\u80fd\u306a\u5024\u306e\u6709\u9650\u30bb\u30c3\u30c8<\/a><\/span>\u306e\u5404\u5024\u3067\u540c\u4e00\u306e\u767a\u751f\u78ba\u7387<\/a><\/span>(\u7b49\u78ba\u7387<\/i>) \u3092\u793a\u3059\u96e2\u6563\u78ba\u7387\u6cd5\u5247<\/a><\/span>\u3067\u3059\u3002<\/p>

\n\"\u96e2\u6563\u7d71\u4e00\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u8aac\u660e<\/h2>

n \u500b\u306e<\/i>\u53ef\u80fd\u306a\u5024k 1<\/sub> \u3001k 2<\/sub> \u3001…\u3001k n<\/sub>\u3092<\/i>\u7b49\u78ba\u7387\u3067\u53d6\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u78ba\u7387\u5909\u6570\u306f<\/a><\/span>\u3001\u4efb\u610f\u306e\u5024k i<\/sub><\/i>\u306e\u78ba\u7387\u304c1\/n<\/i>\u306b\u7b49\u3057\u3044\u5834\u5408\u3001\u4e00\u69d8\u6cd5\u5247<\/b><\/i>\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>

\u5747\u4e00\u306a\u96e2\u6563\u6cd5\u5247\u306e\u7c21\u5358\u306a\u4f8b\u306f\u3001\u6b63\u76f4\u306a\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u3067\u3059\u3002 k<\/i>\u306e\u53ef\u80fd\u306a\u5024\u306f 1\u30012\u30013\u30014\u30015\u30016 \u3067\u3059\u3002\u305d\u3057\u3066\u3001\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u308b\u305f\u3073\u306b\u3001\u4e0e\u3048\u3089\u308c\u305f\u5f97\u70b9\u304c\u51fa\u308b\u78ba\u7387\u306f 1\/6 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>

\u4e00\u69d8\u96e2\u6563\u6cd5\u5247\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570<\/a><\/span>\u306e\u5024\u304c\u5b9f\u6570\u3067\u3042\u308b\u5834\u5408\u3001\u5206\u5e03\u95a2\u6570\u3092\u6c7a\u5b9a\u8ad6\u7684\u5206\u5e03<\/span>\u306e\u89b3\u70b9\u304b\u3089\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066<\/p>

$$ {F(k;a,b,n)={1\\over n}\\sum_{i=1}^n H(k-k_i)} $$<\/div><\/center>

\u3053\u3053\u3067\u3001 H(xx 0<\/sub> ) \u306f<\/i>\u30d8\u30f4\u30a3\u30b5\u30a4\u30c9\u30de\u30fc\u30c1<\/a><\/span>\u95a2\u6570\u3092\u793a\u3057\u3001 x 0<\/sub><\/i>\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u6c7a\u5b9a\u8ad6\u7684\u5206\u5e03\u306e\u5206\u5e03\u95a2\u6570 (\u307e\u305f\u306f\u7d2f\u7a4d\u5206\u5e03) \u3067\u3042\u308a\u3001 x 0<\/sub><\/i>\u306b\u304a\u3051\u308b\u30c7\u30a3\u30e9\u30c3\u30af\u8cea\u91cf<\/a><\/span><\/span>\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u9077\u79fb\u70b9\u3067\u5341\u5206\u306a\u4eee\u5b9a\u304c\u691c\u8a3c\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u307e\u3059\u3002<\/p>

\u4e00\u822c\u7684\u306a\u5834\u5408<\/h2>

\u78ba\u7387<\/i>\u5909\u6570<\/i><\/b><\/i><\/i><\/i>\u200b<\/a><\/span><\/p>

\u91cd\u8981\u306a\u7279\u6b8a\u306a\u30b1\u30fc\u30b9<\/span><\/h3>

\u53cd\u5bfe\u306e\u8868\u306f\u3001 n \u500b<\/i>\u306e\u9023\u7d9a\u3059\u308b\u6574\u6570\u306e\u30bb\u30c3\u30c8\u306b\u95a2\u3059\u308b\u7d71\u4e00\u6cd5\u5247\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3001\u3053\u308c\u306f\u7d71\u4e00\u6cd5\u5247\u306e\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u306b\u3059\u304e\u307e\u305b\u3093\u304c\u3001\u91cd\u8981\u306a\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u3067\u3059\u3002 <\/p>

$$ {\\ A\\ =\\ [\\![a,b]\\!],\\qquad n=b-a+1.} $$<\/div><\/center>

\u78ba\u7387\u3068\u671f\u5f85\u5024\u306e\u8a08\u7b97 (\u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9)<\/span><\/h3>

X \u304c<\/i>\u6709\u9650\u96c6\u5408A<\/i>\u306b\u95a2\u3059\u308b\u4e00\u69d8\u6cd5\u5247\u306b\u5f93\u3046\u5834\u5408\u3001\u6b21\u306e\u6cd5\u5247\u304c<\/i>\u3042\u308b\u3068\u8a00\u308f\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002

$$ {\\scriptstyle\\ \\mathbb{U}_A.\\ } $$<\/div>\u6ce8\u610f\u3057\u307e\u3059<\/p>
$$ {\\ \\mathbb{P}(X=x)\\ =\\ \\mathbb{U}_A(\\{x\\})\\ =\\ \\frac{1\\!\\!1_A(x)}{\\#A},\\ } $$<\/div><\/center>

\u307e\u305f\u306f

$$ {\\scriptstyle\\ 1\\!\\!1_A(.)\\ } $$<\/div>\u306f\u96c6\u5408A<\/i>\u306e\u6307\u6a19\u95a2\u6570\u3092\u793a\u3057\u307e\u3059\u3002\u5b9f\u7528\u7684\u306a\u89b3\u70b9<\/a><\/span>\u304b\u3089<\/a><\/span>\u3001 <\/p>
$$ {\\ \\mathbb{P}(X\\in B)\\ =\\ \\sum_{x\\in B}\\,\\frac{1\\!\\!1_A(x)}{\\#A}\\ =\\ \\frac{\\#(A\\cap B)}{\\#A}.} $$<\/div><\/center>

A<\/i>\u4e0a\u3067\u5b9f\u6570\u5024\u3092\u4f7f\u7528\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\u03c6 \u306e<\/i>\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {\\ \\mathbb{E}\\left[\\phi(X)\\right]\\ =\\ \\frac{1}{\\#A}\\sum_{x\\in A}\\,\\phi(x).} $$<\/div><\/center>

\u3057\u305f\u304c\u3063\u3066\u3001 \u03c6(X)<\/i>\u306e\u671f\u5f85\u5024\u306f\u3001 A<\/i>\u306b\u5bfe\u3059\u308b\u03c6<\/i>\u306e\u5e73\u5747\u5024<\/i>\u306b\u306a\u308a\u307e\u3059\u3002\u53e4\u5178\u7684\u306a\u6e2c\u5b9a\u7406\u8ad6\u306e<\/a><\/span>\u8868\u8a18\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3001\u3053\u308c\u3092\u6b21\u306e\u3088\u3046\u306b\u7ffb\u8a33\u3057\u307e\u3059\u3002 <\/p>

$$ {\\ \\mathbb{P}_X\\ =\\ \\mathbb{U}_A\\ =\\ \\frac{1}{\\#A}\\sum_{x\\in A}\\,\\delta_x,} $$<\/div><\/center>

\u3053\u3053\u3067\u3001 \u03b4 x \u306f<\/sub><\/i>x<\/i>\u306b\u304a\u3051\u308b\u30c7\u30a3\u30e9\u30c3\u30af\u8cea\u91cf<\/span>\u3092\u793a\u3057\u3001\u524d\u8ff0\u306e\u30d8\u30d3\u30fc\u30b5\u30a4\u30c9 \u30de\u30fc\u30c1\u95a2\u6570<\/i>\u306e\u5206\u5e03\u95a2\u6570\u3092\u6301\u3061\u307e\u3059\u3002<\/p><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u062a\u0648\u0632\u064a\u0639 \u0645\u0646\u062a\u0638\u0645 \u0645\u062a\u0642\u0637\u0639 \u2013 arabe<\/a><\/li>
  2. Distribuci\u00f3n uniforme discreta \u2013 asturien<\/a><\/li>
  3. \u0420\u0430\u045e\u043d\u0430\u043c\u0435\u0440\u043d\u0430\u0435 \u0434\u044b\u0441\u043a\u0440\u044d\u0442\u043d\u0430\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u043a\u0430\u0432\u0430\u043d\u043d\u0435 \u2013 bi\u00e9lorusse<\/a><\/li>
  4. Distribuci\u00f3 uniforme discreta \u2013 catalan<\/a><\/li>
  5. Diskrete Gleichverteilung \u2013 allemand<\/a><\/li>
  6. \u0394\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ae \u03bf\u03bc\u03bf\u03b9\u03cc\u03bc\u03bf\u03c1\u03c6\u03b7 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae \u2013 grec<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u96e2\u6563\u7d71\u4e00\u6cd5\u5247\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n