{"id":4769,"date":"2024-08-26T16:02:16","date_gmt":"2024-08-26T07:02:16","guid":{"rendered":"https:\/\/aiknot.jp\/media-top\/?p=4769"},"modified":"2024-08-27T19:24:29","modified_gmt":"2024-08-27T10:24:29","slug":"%e5%8d%98%e7%b4%94%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0%e3%82%a6%e3%82%a9%e3%83%bc%e3%82%af%e3%81%a8%e3%81%af%ef%bc%9f%e5%88%86%e3%81%8b%e3%82%8a%e3%82%84%e3%81%99%e3%81%8f%e8%a7%a3%e8%aa%ac%ef%bc%81","status":"publish","type":"post","link":"https:\/\/aiknot.jp\/media-top\/?p=4769","title":{"rendered":"\u5358\u7d14\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3068\u306f\uff1f\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\uff01"},"content":{"rendered":"\n

\u5358\u7d14\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u6982\u8981<\/h2>\n\n\n\n

\u6700\u3082\u5358\u7d14\u306a\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u30e2\u30c7\u30eb<\/h3>\n\n\n\n

\u4e00\u5b9a\u6642\u9593\u3054\u3068\u306b$+1$\u3001\u53c8\u306f$-1$\u3060\u3051\u79fb\u52d5\u3059\u308b\u5343\u9ce5\u8db3\u306e\u9154\u3063\u6255\u3044\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002\u5b8c\u5168\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u52d5\u304f\u3082\u306e\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u4f8b\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u52d5\u3044\u305f\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

$-1,+1,+1,+1,+1,-1,+1,-1+1,-1-1$<\/p>\n\n\n\n

\u3053\u306e\u6642\u3001\u305d\u308c\u305e\u308c\u306e\u52d5\u304d\u3092\u78ba\u7387\u5909\u6570\u3068\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

$X_1=-1, X_2=+1, X_3=+1, X_4=+1, X_5=+1, X_6=-1,\u2026$<\/p>\n\n\n\n

\u3053\u306e\u3088\u3046\u306a\u78ba\u7387\u5909\u6570\u306e\u4e26\u3073\u3092\u78ba\u7387\u904e\u7a0b\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n

n\u6b69\u76ee\u306b\u9154\u3063\u6255\u3044\u306f\u3069\u3053\u306b\u3044\u308b\u306e\u304b\uff1f<\/h3>\n\n\n\n

\u9154\u3063\u6255\u3044\u306e\u4f4d\u7f6e\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u7dcf\u548c\u3067\u6c7a\u307e\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

$0$\u6b69\u76ee\u3000\u21d2\u3000$0$
$1$\u6b69\u76ee\u3000\u21d2\u3000$-1$
$2$\u6b69\u76ee\u3000\u21d2\u3000$-1+1=0$
$3$\u6b69\u76ee\u3000\u21d2\u3000$-1+1+1=+1$
$4$\u6b69\u76ee\u3000\u21d2\u3000$-1+1+1+1=+2$
\uff1a
<\/p>\n\n\n\n

$n=0$\u3060\u3068$0$\u3001$n=4$\u3060\u3068\u521d\u671f\u4f4d\u7f6e\u304b\u3089$+2$\u306e\u4f4d\u7f6e\u306b\u3044\u307e\u3059\u3002
\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u5f97\u3089\u308c\u305f\u96e2\u6563\u7684\u306a\u6642\u7cfb\u5217\u3092\u300c\u5358\u7d14\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u300d\u3068\u547c\u79f0\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u5358\u7d14\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u671f\u5f85\u5024\u3068\u5206\u6563<\/h2>\n\n\n\n

\u671f\u5f85\u5024<\/h3>\n\n\n\n

\u305d\u308c\u305e\u308c\u306e\u78ba\u7387\u5909\u6570\u306f\u3001$+1$\u304b$-1$\u306e\u3069\u3061\u3089\u304b\u3057\u304b\u53d6\u308a\u307e\u305b\u3093\u3002\u3053\u3053\u3067\u3001$+1$\u3092\u53d6\u308b\u78ba\u7387$p=0.7$\u3001$-1$\u3092\u53d6\u308b\u78ba\u7387$q=0.3$\u3068\u7f6e\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u306e\u3088\u3046\u306a\u4eee\u5b9a\u3092\u7f6e\u304f\u3068\u3001$n$\u6b69\u76ee\u306b\u3069\u3053\u306e\u4f4d\u7f6e\u306b\u3044\u308b\u304b\u306f\u3042\u308b\u7a0b\u5ea6\u4e88\u6e2c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002$+1$\u3092\u53d6\u3063\u3066\u524d\u306b\u9032\u3080\u53ef\u80fd\u6027\u306e\u65b9\u304c\u9ad8\u3044\u305f\u3081\u3001\u6642\u9593\u304c\u9577\u304f\u306a\u308b\u306b\u3064\u308c\u524d\u306b\u9032\u3093\u3067\u3044\u304f\u50be\u5411\u306b\u306a\u308a\u305d\u3046\u3067\u3059\u3002<\/p>\n\n\n\n

\u9154\u3063\u6255\u3044\u306e\u4f4d\u7f6e\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u7dcf\u548c\u306b\u3088\u3063\u3066\u6c7a\u307e\u308b\u305f\u3081\u3001$n$\u6b69\u76ee\u306e\u7dcf\u548c\u3092$S_n$\u3068\u7f6e\u304d\u307e\u3059\u3002$S_n$\u306e\u671f\u5f85\u5024$E(S_n)$\u306f\u3069\u3046\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n\n\n\n

\n

\u8a18\u53f7\u306e\u610f\u5473<\/p>\n\n\n\n

    \n
  • $S$\u306f$Summation$(\u5408\u8a08)<\/li>\n\n\n\n
  • $E$\u306f$Expected\\ value$(\u671f\u5f85\u5024)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

    $E(S_n)=E(X_1+X_2+X_3+X_4\u2026X_n)$<\/p>\n\n\n\n

    \u671f\u5f85\u5024\u306e\u6027\u8cea\u304b\u3089\u300c\u548c\u306e\u671f\u5f85\u5024=\u671f\u5f85\u5024\u306e\u548c\u300d\u3067\u3042\u308b\u305f\u3081\u3001<\/p>\n\n\n\n

    $E(S_n)=E(X_1+X_2+X_3+X_4\u2026X_n)$
    $=E(X_1)+E(X_2)+E(X_3)+E(X_4)\u2026E(X_n)$<\/p>\n\n\n\n

    \u3053\u3053\u3067\u4f8b\u3048\u3070\u671f\u5f85\u5024$E(X_1)$\u3092\u8003\u3048\u308b\u3068\u3001<\/p>\n\n\n\n

    $E(X_1)=+1\u00d7p+(-1)\u00d7q$
    $=p-q$$\u2026(1)$<\/p>\n\n\n\n

    \u3067\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u306e\u671f\u5f85\u5024\u306f\u540c\u3058\u78ba\u7387\u5909\u6570\u3068\u78ba\u7387\u5206\u5e03\u3092\u6301\u3064\u7b49\u4fa1\u306a\u3082\u306e\u3067\u3042\u308b\u304b\u3089\u3001<\/p>\n\n\n\n

    $E(S_n)=E(X_1)+E(X_2)+E(X_3)+E(X_4)\u2026E(X_n)$
    $=nE(X)$
    $=n(p-q)$<\/p>\n\n\n\n

    $p=0.7,q=0.3$\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

    $E(S_n)=n(p-q)$
    $=n(0.7-0.3)$
    $=n\u00d70.4$<\/p>\n\n\n\n

    \u6b69\u6570\u304c\u591a\u304f\u306a\u308b\u3068\u5f90\u3005\u306b\u524d\u306b\u9032\u3093\u3067\u3044\u304f\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

    \u5206\u6563<\/h3>\n\n\n\n

    $n$\u6b69\u76ee\u306e\u9154\u3063\u6255\u3044\u306e\u4f4d\u7f6e\u306e\u5206\u6563\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

    $V(S_n)=V(X_1+X_2+X_3+X_4\u2026X_n)$<\/p>\n\n\n\n

    \n

    \u8a18\u53f7\u306e\u610f\u5473<\/p>\n\n\n\n

      \n
    • $V$\u306f$Variance$(\u5206\u6563)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

      \u78ba\u7387\u5909\u6570\u304c\u72ec\u7acb\u3067\u3042\u308c\u3070\u300c\u548c\u306e\u5206\u6563=\u5206\u6563\u306e\u548c\u300d\u3067\u3042\u308b\u304b\u3089\u3001<\/p>\n\n\n\n

      $V(S_n)=V(X_1+X_2+X_3+X_4\u2026X_n)$
      $=V(X_1)+V(X_2)+V(X_3)+V(X_4)\u2026V(X_n)$<\/p>\n\n\n\n

      \u3053\u3053\u3067\u305d\u308c\u305e\u308c\u306e\u5206\u6563\u306f\u7b49\u4fa1\u3067\u3042\u308b\u304b\u3089\u3001<\/p>\n\n\n\n

      $V(S_n)=V(X_1)+V(X_2)+V(X_3)+V(X_4)\u2026V(X_n)$
      $=nV(X)$$\u2026(2)$<\/p>\n\n\n\n

      \u6b21\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u5206\u6563$V(X)$\u3092\u6c42\u3081\u307e\u3059\u3002
      \u306a\u304a\u3001\u5206\u6563\u306e\u5b9a\u7fa9\u5f0f\u304b\u3089\u5f53\u8a72\u516c\u5f0f\u306e\u5c0e\u51fa\u306f\u30da\u30fc\u30b8\u306e\u672b\u5c3e\u306b\u53c2\u8003\u3068\u3057\u3066\u8a18\u8f09\u3044\u305f\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

      $V(X)=E(X^2)-\\{E(X)\\}^2$$\u2026(3)$
      <\/p>\n\n\n\n

      $X$\u306f$+1,-1$\u3057\u304b\u53d6\u3089\u306a\u3044\u305f\u3081\u3001$X^2$\u306f\u5fc5\u305a$1$\u306b\u306a\u308b\u3002\u3088\u3063\u3066\u3001$(3)$\u306e$E(X^2)$\u306e\u9805\u306f\u6b21\u306e\u901a\u308a\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

      $E(X^2)=X^2\u00d7p+X^2\u00d7q$
      $=(+1)^2\u00d70.7+(-1)^2\u00d70.3=1$<\/p>\n\n\n\n

      \u3053\u306e\u8a08\u7b97\u7d50\u679c\u3068$(1)$\u3092\u3001$(3)$\u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

      $V(X)=1-(p-q)^2$<\/p>\n\n\n\n

      $q=1-p$\u3067\u3042\u308b\u305f\u3081\u3001<\/p>\n\n\n\n

      $=1-(p-(1-p))^2$
      $=1-(p-1+p)^2$
      $=1-(2p-1)^2$
      $=1-(4p^2-4p+1)$
      $=-4p^2+4p$
      $=4p-4p^2$
      $=4p(1-p)$
      $=4pq$$\u2026(4)$<\/p>\n\n\n\n

      $(4)$\u306e\u8a08\u7b97\u7d50\u679c\u3092\u3001$(2)$\u306b\u4ee3\u5165\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

      $V(S_n)=4npq$<\/p>\n\n\n\n

      $p=0.7,q=0.3$\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

      $V(S_n)=4n\u00d70.7\u00d70.3$<\/p>\n\n\n\n

      \u5206\u6563\u3082\u3001\u6b69\u6570\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u5927\u304d\u304f\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

      \u5358\u7d14\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u30b0\u30e9\u30d5<\/h2>\n\n\n\n

      $p=0.7$\u3067\u30d7\u30ed\u30c3\u30c8<\/h3>\n\n\n\n

      \u30a8\u30af\u30bb\u30eb\u3067\u4e71\u6570\u3092\u751f\u6210\u3057\u3001$p=0.7$\u3067\u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      \u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u7279\u5fb4<\/h3>\n\n\n\n

      \u77ed\u671f\u7684\u306b\u306f\u4e88\u6e2c\u4e0d\u53ef\u80fd\u306a\u30e9\u30f3\u30c0\u30e0\u306a\u52d5\u304d\u3092\u3057\u306a\u304c\u3089\u3082\u3001\u9577\u671f\u7684\u306b\u306f$p=0.7$\u306e\u65b9\u5411\u6027\u306b\u63a8\u79fb\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u6642\u9593\u7d4c\u904e\u3068\u5171\u306b\u30d6\u30ec\u3082\u5927\u304d\u304f\u306a\u3063\u3066\u304a\u308a\u3001\u5206\u6563\u304c\u9013\u5897\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

      \u682a\u4fa1\u306e\u52d5\u304d\u3082\u3001\u77ed\u671f\u7684\u306b\u306f\u4e00\u5207\u306e\u4e88\u6e2c\u304c\u4e0d\u53ef\u80fd\u306a\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3067\u3059\u304c\u3001\u9577\u671f\u7684\u306b\u306f\u682a\u5f0f\u767a\u884c\u4f01\u696d\u306e\u696d\u7e3e\u306b\u57fa\u3065\u3044\u3066\u63a8\u79fb\u3059\u308b\u3068\u3044\u308f\u308c\u3066\u304a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306f\u682a\u4fa1\u306e\u52d5\u304d\u3092\u64ec\u5236\u3059\u308b\u306e\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u4e00\u822c\u7684\u306a\u682a\u4fa1\u30e2\u30c7\u30eb\u306f\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u8003\u3048\u65b9\u304b\u3089\u5c0e\u304b\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

      \u88dc\u8db3<\/h2>\n\n\n\n

      \u4f7f\u7528\u3057\u305f\u5206\u6563\u306e\u516c\u5f0f\u306e\u5c0e\u51fa<\/h3>\n\n\n\n

      \u5206\u6563\u306f\u5e73\u5747\u5024\u3068\u306e\u5dee\u3092\u53d6\u3063\u3066\u4e8c\u4e57\u3057\u305f\u3082\u306e\u306a\u306e\u3067\u6b21\u306e\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

      $V(X)=E((X-\u03bc)^2)$<\/p>\n\n\n\n

      \n
        \n
      • $\u03bc$\u306f\u5e73\u5747\u3067$\u03bc=E(X)$<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

        $V(X)=E((X-\u03bc)^2)$
        $=E(X^2-2\u03bcX+\u03bc^2)$<\/p>\n\n\n\n

        \u671f\u5f85\u5024\u306e\u6027\u8cea\u304b\u3089\u300c\u548c\u306e\u671f\u5f85\u5024\uff1d\u671f\u5f85\u5024\u306e\u548c\u300d\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

        $=E(X^2-2\u03bcX+\u03bc^2)$
        $=E(X^2)-E(2\u03bcX)+E(\u03bc^2)$<\/p>\n\n\n\n

        \u671f\u5f85\u5024\u306e\u6027\u8cea\u304b\u3089\u5b9a\u6570\u306f\u5916\u306b\u51fa\u305b\u308b\u305f\u3081\u3001<\/p>\n\n\n\n

        $=E(X^2)-E(2\u03bcX)+E(\u03bc^2)$
        $=E(X^2)-2\u03bcE(X)+E(\u03bc^2)$<\/p>\n\n\n\n

        $E(\u03bc^2)$\u306e\u9805\u306b\u7740\u76ee\u3059\u308b\u3068\u3001$\u03bc$\u306f\u78ba\u7387\u5909\u6570\u3067\u306f\u306a\u304f\u5b9a\u6570\u306a\u306e\u3067100%$\u03bc^2$\u306e\u5024\u3057\u304b\u53d6\u3089\u305a\u3001\u671f\u5f85\u5024\u3082$E(\u03bc^2)=\u03bc^2$\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001$\u03bc=E(X)$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

        $=E(X^2)-2\u03bcE(X)+E(\u03bc^2)$
        $=E(X^2)-2\u03bc\u00d7\u03bc+\u03bc^2$
        $=E(X^2)-2\u03bc^2+\u03bc^2$
        $=E(X^2)-\u03bc^2$
        $=E(X^2)-\\{E(X)\\}^2$<\/p>\n","protected":false},"excerpt":{"rendered":"

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