{"id":2588,"date":"2018-08-24T17:45:40","date_gmt":"2018-08-24T08:45:40","guid":{"rendered":"https:\/\/pandanote.info\/?p=2588"},"modified":"2022-08-07T00:37:50","modified_gmt":"2022-08-06T15:37:50","slug":"%e6%a8%99%e6%ba%96%e6%ad%a3%e8%a6%8f%e5%88%86%e5%b8%83%e3%81%ae%e7%a2%ba%e7%8e%87%e5%af%86%e5%ba%a6%e9%96%a2%e6%95%b0%e3%82%92%e3%83%86%e3%82%a4%e3%83%a9%e3%83%bc%e5%b1%95%e9%96%8b%e3%81%97%e3%81%a6","status":"publish","type":"post","link":"https:\/\/pandanote.info\/?p=2588","title":{"rendered":"\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3057\u3066\u304b\u3089\u7a4d\u5206\u3057\u3066\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u6c42\u3081\u3066\u307f\u305f\u3002"},"content":{"rendered":"<p><script type=\"text\/x-mathjax-config\">MathJax.Hub.Config({ TeX: { extensions: [\"color.js\"] }});<\/script><\/p>\n<h2>\u306f\u3058\u3081\u306b<\/h2>\n<p><a href=\"https:\/\/pandanote.info\/?p=2537\">\u524d\u306e\u8a18\u4e8b<\/a>\u3067\u6b63\u898f\u5206\u5e03\u306b\u5f93\u30462\u500b\u306e\u72ec\u7acb\u306a\u78ba\u7387\u5909\u6570\u306e\u548c\u3068\u5dee\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>Google\u5148\u751f\u306b\u805e\u3044\u3066\u307f\u305f\u308a\u3001\u601d\u3044\u51fa\u3057\u306a\u304c\u3089\u66f8\u3044\u3066\u3044\u308b\u305f\u3081\u306b\u3068\u3053\u308d\u3069\u3053\u308d\u7528\u8a9e\u306e\u4f7f\u3044\u65b9\u304c\u602a\u3057\u3044\u90e8\u5206\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u305d\u306e\u3042\u305f\u308a\u306f\u6c17\u3065\u304d\u6b21\u7b2c\u4fee\u6b63\u3057\u307e\u3059\u3002<\/p>\n<p><a href=\"https:\/\/pandanote.info\/?p=2537\">\u524d\u306e\u8a18\u4e8b<\/a>\u3067\u3061\u3087\u3063\u3068\u30a8\u30f3\u30b8\u30f3\u304c\u304b\u304b\u3063\u3066\u304d\u305f\u3068\u3053\u308d\u3067\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3057\u3001\u3055\u3089\u306b\u305d\u3044\u3064\u3092\u7a4d\u5206\u3057\u3066\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>\u3064\u3044\u3067\u306b\u53ce\u675f\u5224\u5b9a\u306e\u3068\u3053\u308d\u3067\u5c11\u3057\u5bc4\u308a\u9053\u3092\u3057\u307e\u3059\u3002<\/p>\n<h2>\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3057\u307e\u3059\u3002<\/h2>\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u51aa\u4e57\u53ca\u3073\u968e\u4e57\u306e\u8a08\u7b97\u5f0f\u304c\u983b\u7e41\u306b\u767b\u5834\u3057\u307e\u3059\u304c\u3001$0^0 = 1, 0! = 1, 0!! = 1$\u3068\u3057\u307e\u3059\u3002<\/p>\n<h3>\u6307\u6570\u95a2\u6570\u306e\u30c6\u30a4\u30e9\u30fc\u5c55\u958b<\/h3>\n<p>\u6307\u6570\u95a2\u6570\u306e$x=0$\u306e\u307e\u308f\u308a\u306b\u304a\u3051\u308b\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u306f(\\ref{eq:exptaylor})\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002<br \/>\n\\begin{align}<br \/>\ne^x &#038;= \\sum_{n=0}^{\\infty}\\frac{x^n}{n!} \\label{eq:exptaylor}<br \/>\n\\end{align}<\/p>\n<p>\u6b21\u7bc0\u4ee5\u964d\u306e\u8a71\u306e\u5c55\u958b\u306e\u90fd\u5408\u4e0a\u3001$e^{-x}$\u3092$x=0$\u306e\u307e\u308f\u308a\u3067\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3057\u305f\u5f0f\u304c\u5fc5\u8981\u306b\u306a\u308b\u306e\u3067\u3001\u4ee5\u4e0b((\\ref{eq:exptaylorminus})\u5f0f)\u306b\u793a\u3057\u3066\u304a\u304d\u307e\u3059\u3002<br \/>\n\\begin{align}<br \/>\ne^{-x} &#038;= \\sum_{n=0}^{\\infty}(-1)^n\\frac{x^n}{n!} \\label{eq:exptaylorminus}<br \/>\n\\end{align}<\/p>\n<h3>\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u30c6\u30a4\u30e9\u30fc\u5c55\u958b<\/h3>\n<p>\u6b21\u306b\u3001\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e$x=0$\u306e\u307e\u308f\u308a\u306b\u304a\u3051\u308b\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\u3068\u3044\u3063\u3066\u3082\u3001\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u306e(\u4e00\u822c\u7684\u306a)\u5c55\u958b\u5f0f<br \/>\n\\begin{align}<br \/>\nf(x) &#038;= \\sum_{n=0}^{\\infty}(-1)^n\\frac{x^n}{n!}f^{(n)}(0) \\label{eq:taylor}<br \/>\n\\end{align}<br \/>\n\u306b<br \/>\n\\begin{align}<br \/>\np(x) &#038;= \\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{x^2}{2}} \\label{eq:gaussian}<br \/>\n\\end{align}<br \/>\n\u3092\u76f4\u63a5\u5f53\u3066\u306f\u3081\u3088\u3046\u3068\u3057\u3066\u3001$f^{\\prime}(x),f^{\\prime\\prime}(x),f^{(3)}(x),\\cdots$\u3092\u9806\u6b21\u8a08\u7b97\u3057\u3066\u307f\u305f\u3068\u3053\u308d\u3067\u53ce\u62fe\u304c\u3064\u304b\u306a\u304f\u306a\u308b\u3060\u3051\u306a\u306e\u3067\u3001\u3053\u3053\u306f\u524d\u7bc0\u306e\u7d50\u679c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<p>(\\ref{eq:exptaylorminus}),(\\ref{eq:taylor})\u53ca\u3073(\\ref{eq:gaussian})\u5f0f\u3092\u3058\u30fc\u3063\u3068\u898b\u6bd4\u3079\u308b\u3068\u3001$f(x) = e^{-x}$\u3068\u304a\u3044\u3066\u3001\u3055\u3089\u306b$f\\left(\\displaystyle\\frac{x^2}{2}\\right)$\u3092(\\ref{eq:exptaylorminus})\u5f0f\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\u3001<br \/>\n\\begin{align}<br \/>\nf\\left(\\displaystyle\\frac{x^2}{2}\\right) &#038;= \\frac{1}{\\sqrt{2\\pi}}\\sum_{n=0}^{\\infty}\\frac{(-1)^n}{n!}\\left(\\displaystyle\\frac{x^2}{2}\\right)^n \\nonumber \\\\<br \/>\n&#038;= \\frac{1}{\\sqrt{2\\pi}}\\sum_{n=0}^{\\infty}\\frac{(-1)^n\\,x^{2n}}{(2n)!!} \\label{eq:gausstaylor}<br \/>\n\\end{align}<br \/>\n(\u305f\u3060\u3057\u3001$(2n)!! = \\displaystyle\\prod_{k=1}^n2k$\u3068\u3057\u307e\u3059\u3002)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u53ce\u675f\u3059\u308b\u3053\u3068\u306e\u78ba\u8a8d\u3002<\/h3>\n<p>\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f(\\ref{eq:gausstaylor})\u5f0f\u306e\u901a\u308a\u306b\u8a08\u7b97\u304c\u3067\u304d\u305d\u3046\u3067\u3059\u304c\u3001(\\ref{eq:gausstaylor})\u5f0f\u306e\u53f3\u8fba\u304c\u53ce\u675f\u3059\u308b\u3053\u3068\u3092\u793a\u3055\u306a\u3044\u3068\u4f7f\u3044\u7269\u306b\u306a\u308a\u307e\u305b\u3093\u3002(\\ref{eq:gausstaylor})\u5f0f\u306e\u5de6\u8fba\u3092\u3042\u3089\u305f\u3081\u3066$f(x)$\u3068\u7f6e\u304d\u306a\u304a\u3057\u3066\u3001\u53f3\u8fba\u3092$x$\u306e\u7d1a\u6570\u3068\u8003\u3048\u308b\u3068\u3001\u7d1a\u6570\u306e\u5404\u9805\u306e\u4fc2\u6570$\\{a_n\\} (n \\ge 0)$\u306f<br \/>\n\\begin{align}<br \/>\na_n &#038;=<br \/>\n\\begin{cases}<br \/>\n\\displaystyle\\frac{1}{\\sqrt{2\\pi}}\\displaystyle\\frac{(-1)^k}{(2k)!!} &#038; (n: even, n = 2k) \\\\<br \/>\n0 &#038; (otherwise)<br \/>\n\\end{cases} \\label{eq:coefficient}<br \/>\n\\end{align}<br \/>\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u3001<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%80%E3%83%A9%E3%83%B3%E3%83%99%E3%83%BC%E3%83%AB%E3%81%AE%E5%8F%8E%E6%9D%9F%E5%88%A4%E5%AE%9A%E6%B3%95\">\u30c0\u30e9\u30f3\u30d9\u30fc\u30eb\u306e\u53ce\u675f\u5224\u5b9a\u6cd5<\/a>\u3092\u4f7f\u3044\u305f\u3044\u2026 \u3068\u3053\u308d\u3067\u306f\u3042\u308a\u307e\u3059\u304c\u3001(\\ref{eq:coefficient})\u5f0f\u3088\u308a\u3001\u96a3\u63a5\u3059\u308b\u9805\u306e\u3069\u3061\u3089\u304b\u7247\u65b9\u304c0\u306b\u306a\u308a\u307e\u3059\u306e\u3067\u3001\u305d\u306e\u307e\u307e\u3067\u306f\u4f7f\u7528\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u3053\u3053\u306f<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%82%B3%E3%83%BC%E3%82%B7%E3%83%BC%E3%81%AE%E5%86%AA%E6%A0%B9%E5%88%A4%E5%AE%9A%E6%B3%95\">\u30b3\u30fc\u30b7\u30fc\u306e\u51aa\u6839\u5224\u5b9a\u6cd5<\/a>\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002(\\ref{eq:coefficient})\u5f0f\u306e$a_n$\u3088\u308a\u3001<br \/>\n\\begin{align}<br \/>\n\\sqrt[n]{|a_n|} &#038;=<br \/>\n\\begin{cases}<br \/>\n\\displaystyle\\frac{1}{\\sqrt[2n]{2\\pi}}\\displaystyle\\frac{1}{\\sqrt[n]{n!!}} > 0 &#038; (n: even, n = 2k) \\\\<br \/>\n0 &#038; (otherwise)<br \/>\n\\end{cases}<br \/>\n\\end{align}<br \/>\n\u3068\u306a\u308b\u3053\u3068\u3068\u3001$\\displaystyle\\lim_{n \\to \\infty} \\displaystyle\\frac{1}{\\sqrt[n]{n!!}} = 0$\u3067\u3042\u308b\u3053\u3068(\u8a3c\u660e\u306f<a href=\"https:\/\/pandanote.info\/?p=2910\">\u3053\u3061\u3089<\/a>\u53c2\u7167\u2026 \u3068\u6700\u521d\u306f\u66f8\u3044\u3066\u3044\u305f\u306e\u3067\u3059\u304c\u3001\u53c2\u7167\u5148\u3067\u306f$\\displaystyle\\lim_{n \\to \\infty} \\displaystyle\\frac{1}{\\sqrt[n]{\\color{red}{n!}}} = 0$\u3092\u8a3c\u660e\u3057\u3066\u307e\u3057\u305f(\u6c57)\u3002\u3053\u308c\u3092\u3082\u3068\u306b$\\displaystyle\\lim_{n \\to \\infty} \\displaystyle\\frac{1}{\\sqrt[n]{n!!}} = 0$\u306f\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002\u8a3c\u660e\u306e\u65b9\u6cd5\u306f<a href=\"https:\/\/pandanote.info\/?p=2910\">\u3053\u3061\u3089\u306b\u66f8\u304d\u307e\u3057\u305f<\/a>\u3002)\u304b\u3089\u3001$\\displaystyle\\limsup_{n \\to \\infty} a_n = 0 < 1$\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066(\\ref{eq:gausstaylor})\u5f0f\u306e\u7d1a\u6570\u306f($x$\u306b\u3064\u3044\u3066)\u53ce\u675f\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\n\n\n<h2>\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/h2>\n<p>\u3053\u306e\u7bc0\u3067\u306f\u3001\u524d\u7bc0\u306e\u7d50\u679c\u3092\u5229\u7528\u3057\u3066\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u306a\u304a\u3001\u3053\u306e\u7bc0\u3067\u306f\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092$P(x)$\u3068\u7f6e\u304d\u307e\u3059\u3002<\/p>\n<h3>\u7a4d\u5206\u3057\u307e\u3059\u3002<\/h3>\n<p>\u307e\u305a\u3001\u4e0d\u5b9a\u7a4d\u5206\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002(\\ref{eq:gausstaylor})\u5f0f\u306f$x$\u306b\u3064\u3044\u3066\u9805\u5225\u7a4d\u5206\u3067\u304d\u307e\u3059\u306e\u3067\u3001\u7a4d\u5206\u5b9a\u6570\u3092C\u3068\u3059\u308b\u3068\u3001<br \/>\n\\begin{align}<br \/>\nP(x) &#038;= \\int p(x) dx \\nonumber \\\\<br \/>\n&#038;= \\frac{1}{\\sqrt{2\\pi}}\\int \\left\\{ \\sum_{n=0}^{\\infty}\\frac{(-1)^n\\,x^{2n}}{(2n)!!} \\right\\}dx \\nonumber \\\\<br \/>\n&#038;= \\frac{1}{\\sqrt{2\\pi}}\\sum_{n=0}^{\\infty}\\frac{(-1)^n}{(2n+1)\\,(2n)!!}x^{2n+1}+C<br \/>\n\\end{align}<br \/>\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u6b21\u306b\u3001$P(0)=1\/2$\u3067\u3042\u308b\u3053\u3068\u3092\u5229\u7528\u3059\u308b\u3068$C=1\/2$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001$P(x)$\u306f(\\ref{eq:solution})\u5f0f\u306e\u3088\u3046\u306b\u5b9a\u307e\u308a\u307e\u3059\u3002<br \/>\n\\begin{align}<br \/>\nP(x) &#038;= \\frac{1}{\\sqrt{2\\pi}}\\sum_{n=0}^{\\infty}\\frac{(-1)^n}{(2n+1)\\,(2n)!!}x^{2n+1}+\\frac{1}{2} \\label{eq:solution}<br \/>\n\\end{align}<\/p>\n<h3>\u3082\u3046\u3061\u3087\u3044\u5909\u5f62\u3002<\/h3>\n<p>\u6570\u5b66\u7684\u306b\u306f(\\ref{eq:solution})\u5f0f\u306e\u5f62\u3067\u826f\u3044\u3088\u3046\u306a\u6c17\u3082\u3057\u307e\u3059\u304c\u3001\u3053\u3053\u307e\u3067\u8a08\u7b97\u3067\u304d\u308b\u3068\u3001\u5b9f\u969b\u306b\u691c\u7b97\u3057\u3066\u307f\u305f\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067$a_n = \\displaystyle\\frac{(-1)^n}{(2n+1)\\,(2n)!!}$\u3068\u304a\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3059\u3002<\/p>\n<p>\u3059\u308b\u3068\u3001$a_0 = 1$\u306a\u306e\u3067\u3001<br \/>\n\\begin{align}<br \/>\nP(x) &#038;= \\frac{1}{\\sqrt{2\\pi}} \\sum_{n=0}^{\\infty} a_n x^{2n+1}+\\frac{1}{2} \\nonumber \\\\<br \/>\n&#038;= \\frac{1}{\\sqrt{2\\pi}} \\left\\{ a_0x + a_0x\\sum_{n=1}^{\\infty} \\left( \\prod_{k=0}^{n-1}\\frac{a_{k+1}}{a_k}x^2 \\right) \\right\\}+\\frac{1}{2} \\nonumber \\\\<br \/>\n&#038;= \\frac{x}{\\sqrt{2\\pi}} \\left\\{ 1 + \\sum_{n=1}^{\\infty} \\left( \\prod_{k=0}^{n-1}\\frac{-(2k+1)}{(2k+2)(2k+3)}x^2 \\right) \\right\\}+\\frac{1}{2} \\label{eq:solutionseries}<br \/>\n\\end{align}<br \/>\n\u53ce\u675f\u304c\u3042\u307e\u308a\u901f\u304f\u306a\u3055\u305d\u3046\u306a\u6c17\u3082\u3057\u307e\u3059\u304c\u3001\u4e0a\u5f0f\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3068\u7d1a\u6570\u306e\u524d\u306e\u9805\u306e\u4fc2\u6570\u306e\u8a08\u7b97\u7d50\u679c\u53ca\u3073\u5909\u6570$x$\u4e26\u3073\u306b\u9805\u756a\u53f7$k$\u306e\u307f\u3092\u4f7f\u3063\u3066\u6b21\u306e\u9805\u306e\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2>\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u66f8\u3044\u3066\u691c\u7b97\u3067\u3059\u3002<\/h2>\n<p>(\\ref{eq:solutionseries})\u5f0f\u304c\u5c0e\u3051\u305f\u306e\u3067\u3001\u6b63\u3057\u3044\u304b\u3069\u3046\u304b\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u66f8\u3044\u3066\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002\u306a\u304a\u3001\u30c6\u30b9\u30c8\u7528\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u3059\u306e\u3067\u3001\u30c7\u30d0\u30c3\u30b0\u7528\u3068\u601d\u3057\u304d\u51fa\u529b\u304c\u6b8b\u3063\u3066\u3044\u308b\u306e\u306f\u3054\u5bb9\u8d66\u3044\u305f\u3060\u3051\u308c\u3070\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>\u30b3\u30fc\u30c9\u3092\u5dee\u3057\u66ff\u3048\u307e\u3057\u305f\u3002[2018\/09\/03\u8ffd\u8a18,2018\/09\/16\u8a08\u7b97\u5f0f\u3092\u8a02\u6b63]<\/h3>\n<p>normDist\u95a2\u6570\u4e2d\u306ewhile\u6587\u306e\u30eb\u30fc\u30d7\u306e\u7d99\u7d9a\u6761\u4ef6\u3092\u5909\u5316\u7387\u306e\u7d76\u5bfe\u5024($a_nx^{2n+1}$\u3092\u76f4\u524d\u306e\u9805($n-1$\u9805)\u307e\u3067\u306e$P(x)$\u306e\u8a08\u7b97\u7d50\u679c\u3067\u5272\u3063\u305f\u5024\u306e\u7d76\u5bfe\u5024)\u304c$10^{-12}$\u4ee5\u4e0a\u3067\u3042\u308b\u5834\u5408\u306b\u5909\u66f4\u3057\u3066\u3044\u307e\u3059(\u306a\u304a\u3001\u30b3\u30fc\u30c9\u306e\u5dee\u3057\u66ff\u3048\u524d\u306f$|a_nx^{2n+1}| > 10^{-12}$\u3067\u3042\u308b\u5834\u5408\u3068\u3057\u3066\u3044\u307e\u3057\u305f)\u3002<\/p>\n<p>\u3053\u308c\u306b\u4f34\u3044\u3001\u3044\u308f\u3086\u308b\u300c\u30bc\u30ed\u5272\u308a\u30a8\u30e9\u30fc\u300d\u304c\u767a\u751f\u3059\u308b\u306e\u3092\u9632\u6b62\u3059\u308b\u305f\u3081\u3001normDist\u95a2\u6570\u306e\u5f15\u6570\u306b0\u304c\u6307\u5b9a\u3055\u308c\u305f\u5834\u5408\u306b\u306f\u8a08\u7b97\u3092\u884c\u308f\u305a\u306b0.5\u3092\u8fd4\u3059\u305f\u3081\u306e\u30b3\u30fc\u30c9\u3092\u95a2\u6570\u306e\u5148\u982d\u90e8\u5206\u306b\u8ffd\u52a0\u3057\u307e\u3057\u305f\u3002<\/p>\n<p><script src=\"https:\/\/gist.github.com\/pandanote-info\/cf3d004aff110129d6fb8ac631f814cc.js\"><\/script><\/p>\n<h3>Excel\u3068\u7b54\u3048\u5408\u308f\u305b\u3002<\/h3>\n<p>\u5b9f\u306fExcel\u306e\u95a2\u6570\u306b\u540c\u69d8\u306e\u8a08\u7b97\u3092\u884c\u3046\u3082\u306e(NORM.S.DIST\u95a2\u6570)\u304c\u3042\u308a\u307e\u3059\u306e\u3067\u3001\u305d\u306e\u7d50\u679c\u3068\u7167\u3089\u3057\u5408\u308f\u305b\u3066\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<br \/>\n<a href=\"https:\/\/pandanote.info\/?attachment_id=2618\" rel=\"attachment wp-att-2618\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pandanote.info\/wordpress\/wp-content\/uploads\/2018\/08\/normdist_scene1-300x199.png\" alt=\"\" width=\"300\" height=\"199\" class=\"alignnone size-medium wp-image-2618\" srcset=\"https:\/\/pandanote.info\/wordpress\/wp-content\/uploads\/2018\/08\/normdist_scene1-300x199.png 300w, https:\/\/pandanote.info\/wordpress\/wp-content\/uploads\/2018\/08\/normdist_scene1-768x510.png 768w, https:\/\/pandanote.info\/wordpress\/wp-content\/uploads\/2018\/08\/normdist_scene1-660x439.png 660w, https:\/\/pandanote.info\/wordpress\/wp-content\/uploads\/2018\/08\/normdist_scene1.png 945w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><br \/>\n\u6b63\u3057\u3044\u8a08\u7b97\u7d50\u679c\u3092\u8fd4\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3057\u305f\u3002(\uff40\u30fb\u03c9\u30fb\u00b4)\uff7c\uff6c\uff77\uff70\uff9d<\/p>\n<h2>\u307e\u3068\u3081<\/h2>\n<p>\u3053\u3053\u307e\u3067\u306e\u8003\u5bdf\u3067\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u304c\u6b63\u898f\u5206\u5e03\u3067\u3042\u308b\u78ba\u7387\u5909\u6570\u304c\u3042\u308b\u5024$x$\u4ee5\u4e0b\u306e\u5024\u3092\u3068\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u8a08\u7b97\u5f0f\u3067\u3001\u304b\u3064\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u6bd4\u8f03\u7684\u5bb9\u6613\u306b\u5b9f\u88c5\u3067\u304d\u308b\u3082\u306e\u3092\u5c0e\u51fa\u3057\u3001\u5b9f\u969b\u306b\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066\u5b9f\u88c5\u3057\u3066\u52d5\u4f5c\u3092\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n<p>\u524d\u9805\u306e\u52d5\u4f5c\u78ba\u8a8d\u3067$x=4.0$\u3067\u5c0f\u6570\u70b9\u4ee5\u4e0b10\u6841\u7a0b\u5ea6\u306e\u7cbe\u5ea6\u306e\u8a08\u7b97\u304c36\u56de\u306e\u53cd\u5fa9\u8a08\u7b97($a_0$\u306e\u8a08\u7b97\u3092\u9664\u304f)\u3067\u3067\u304d\u3066\u3044\u305f\u306e\u3067\u3001\u6700\u521d\u306e\u4e88\u60f3\u3088\u308a\u306f\u8a08\u7b97\u306e\u52b9\u7387\u306f\u826f\u3044\u3068\u601d\u3044\u307e\u3059\u3002$x$\u306b10\u3068\u304b100\u3068\u304b\u3068\u3044\u3063\u305f\u6975\u7aef\u306a\u5024\u3092\u6307\u5b9a\u3055\u308c\u3066\u3057\u307e\u3063\u305f\u5834\u5408\u306b\u306f\u3001\u7cbe\u5ea6\u3068\u306e\u517c\u306d\u5408\u3044\u3067\u53cd\u5fa9\u8a08\u7b97\u3092\u884c\u308f\u305a\u30011.0(\u307e\u305f\u306f0.0)\u3092\u8fd4\u3057\u3066\u3057\u307e\u3046\u5b9f\u88c5\u306b\u3059\u308b\u306e\u3082\u3042\u308a\u3060\u3068\u306f\u601d\u3044\u307e\u3059\u304c\u3001\u305d\u308c\u306f\u30b7\u30b9\u30c6\u30e0\u306a\u3069\u306b\u95a2\u6570\u3092\u5b9f\u88c5\u3057\u3066\u7d44\u307f\u8fbc\u3080\u3068\u304d\u306b\u89e3\u6c7a\u305b\u306d\u3070\u306a\u3089\u306a\u3044\u8ab2\u984c\u3067\u3059\u306d\u3002<\/p>\n<p>\u3053\u306e\u8a18\u4e8b\u306f\u4ee5\u4e0a\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b \u524d\u306e\u8a18\u4e8b\u3067\u6b63\u898f\u5206\u5e03\u306b\u5f93\u30462\u500b\u306e\u72ec\u7acb\u306a\u78ba\u7387\u5909\u6570\u306e\u548c\u3068\u5dee\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002 Google\u5148\u751f\u306b\u805e\u3044\u3066\u307f\u305f\u308a\u3001\u601d\u3044\u51fa\u3057\u306a\u304c\u3089\u66f8\u3044\u3066\u3044\u308b\u305f\u3081\u306b\u3068\u3053\u308d\u3069\u3053\u308d\u7528\u8a9e\u306e\u4f7f\u3044\u65b9\u304c\u602a\u3057\u3044\u90e8\u5206\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u305d\u306e\u3042\u305f\u308a\u306f\u6c17\u3065\u304d\u6b21\u7b2c\u4fee\u6b63\u3057\u307e\u3059\u3002 \u524d\u306e\u8a18\u4e8b\u3067\u3061\u3087\u3063\u3068\u30a8\u30f3\u30b8\u30f3\u304c\u304b\u304b\u3063\u3066\u304d\u305f\u3068\u3053\u308d\u3067\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3057\u3001\u3055\u3089\u306b\u305d\u3044\u3064\u3092\u7a4d\u5206\u3057\u3066\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u8a08\u7b97\u3057\u2026 <span class=\"read-more\"><a href=\"https:\/\/pandanote.info\/?p=2588\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":2618,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,15],"tags":[],"class_list":["post-2588","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-13","category-pc"],"_links":{"self":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/2588","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2588"}],"version-history":[{"count":60,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/2588\/revisions"}],"predecessor-version":[{"id":9346,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/2588\/revisions\/9346"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/media\/2618"}],"wp:attachment":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2588"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2588"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2588"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}