{"id":1670,"date":"2020-07-05T11:00:00","date_gmt":"2020-07-05T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=1670"},"modified":"2020-08-11T11:11:03","modified_gmt":"2020-08-11T02:11:03","slug":"dud-mv","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/dud-mv","title":{"rendered":"\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u671f\u5f85\u5024\u3068\u5206\u6563\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011"},"content":{"rendered":"\n

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n

\u3053\u306e\u8a18\u4e8b\u3067\u306f\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u65b9\u306f\u662f\u975e\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002\u305d\u306e\u4ed6\u306e\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u57fa\u672c\u60c5\u5831\u306f\uff1c\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\uff1e<\/a>\u306e\u8a18\u4e8b\u3092\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u203b\u3000\u4e00\u69d8\u5206\u5e03\u306f\u9023\u7d9a\u578b\u3082\u3042\u308a\u307e\u3059\u3002\u9023\u7d9a\u578b\u306e\u4e00\u69d8\u5206\u5e03\u306b\u3064\u3044\u3066\u306f\uff1c\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09\uff1e\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563<\/h3>\n\n\n\n
\u671f\u5f85\u5024\u3068\u5206\u6563<\/strong><\/div>\n
\u4e00\u69d8\u5206\u5e03\\(X\\sim U(n)\\)\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n
\\begin{align}\n\\mathrm{E}[X]=\\frac{n}{2},\\ \\ \\ \\mathrm{Var}[X]=\\frac{n(n+2)}{12}\n\\end{align}<\/div>\n<\/div>\n\n\n\n

\u671f\u5f85\u5024\u30fb\u5206\u6563\u3092\u6c42\u3081\u308b\u969b\u306b\u306f\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\uff1e<\/a>\u304a\u3088\u3073\uff1c\u5206\u6563\u306e\u5b9a\u7fa9\uff1e<\/a>\u3092\u4f7f\u7528\u3059\u308b\u306e\u3067\u3001\u899a\u3048\u3066\u3044\u306a\u3044\u65b9\u306f\u8a3c\u660e\u3092\u8aad\u3080\u524d\u306b\u4e00\u5ea6\u3001\u76ee\u3092\u901a\u3057\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u3000<\/p>\n\n\n\n

\u3000<\/p>\n\n\n\n

\u8a3c\u660e<\/h4>\n\n\n\n

\u78ba\u7387\u5909\u6570\u304c\\(X\\sim U(n)\\)\u306b\u5f93\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\\(X\\)\u306e\u78ba\u7387\u95a2\u6570\u306f

\\begin{align}
f(x)=\\left\\{
\\begin{array}{ccc}
& \\displaystyle\\frac{1}{n+1} &\uff080 \\leq x \\leq n\uff09\\\\
& 0 &\uff08\u305d\u306e\u4ed6\uff09
\\end{array}\\right.
\\end{align}<\/div>
\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u306f\uff1c\u4e00\u69d8\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831\uff1e<\/a>\u3092\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002
\u3000\u307e\u305a\u3001\u671f\u5f85\u5024\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002
\\begin{align}
\\mathrm{E}[X] &= \\sum_{x=0}^{n}xf(x) \\\\
&= \\sum_{x=0}^{n}x\\cdot\\frac{1}{n+1} \\\\
&= \\frac{n(n+1)}{2}\\cdot\\frac{1}{(n+1)} \\\\
&= \\frac{n}{2}
\\end{align}<\/div>
\u304c\u6210\u7acb\u3057\u307e\u3059\uff08\u7b49\u5dee\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3057\u305f\uff09\u3002
\u3000\u3042\u3068\u306f\u5206\u6563\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\uff1c\u5206\u6563\u306e\u5b9a\u7fa9\uff1e<\/a>\u306e\u8a18\u4e8b\u304b\u3089\u5206\u6563\u306f
\\begin{align}
\\mathrm{Var}[X] &= \\mathrm{E}[X^{2}]-\\mathrm{E}[X]^{2}
\\end{align}<\/div>
\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3001\\(\\mathrm{E}[X^{2}]\\)\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3088\u3063\u3066
\\begin{align}
\\mathrm{E}[X^{2}] &= \\sum_{x=0}^{n}x^{2}f(x) \\\\
&= \\sum_{x=0}^{n}x^{2}\\cdot\\frac{1}{n+1} \\\\
&= \\frac{n(n+1)(2n+1)}{6}\\cdot\\frac{1}{(n+1)} \\\\
&= \\frac{n(2n+1)}{6}
\\end{align}<\/div>
\u3068\u306a\u308b\u3053\u3068\u304b\u3089\u3001\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306e\u5206\u6563\u306f
\\begin{align}
\\mathrm{Var}[X] = \\frac{n(n+2)}{12}
\\end{align}<\/div>
\u304c\u6210\u7acb\u3057\u307e\u3059\uff08\u4e8c\u4e57\u548c\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3057\u305f\uff09\u3002<\/p>\n\n\n\n

\u25a1<\/p>\n","protected":false},"excerpt":{"rendered":"

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