MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C82EB7.CB84CCB0" このドキュメントは単一ファイル Web ページ (Web アーカイブ ファイル) です。お使いのブラウザ、またはエディタは Web アーカイブ ファイルをサポートしていません。Microsoft Internet Explorer など、Web アーカイブをサポートするブラウザをダウンロードしてください。 ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本

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マスタ タイトルの書式設定
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第 2 レベル
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マスタ タイトルの書式設定
マスタ サブタイトルの書式設定
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<ヘッダー>= ;
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<日付/時刻>
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<#>
------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
データ分布と予測
母集団と標本
堀田　敬介
2007/11/16,Fri.
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BRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAF FFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUU UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRR QAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFA BRRRQAUUUUAFFFFABRRRQAUUUUAf/9k= ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0043.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
Contents
3D"*"母集団と標本<= /span>
3D"*"母平均，母分= Uの推測
3D"*"標本平均
3D"*"標本平均の従= ､確率分布
3D"*"大数の法則，= 心極限定理
3D"*"標準正規分布= Ct分布
3D"*"標本分散
3D"*"標本分散の従= ､確率分布
3D"*"χ２分布&= #13;
3D"*"母比率の推測<= /span>
3D"*"標本比率
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母集団と標本：統計的推論
3D"*"推測統計学 stati= stical estimate / statistical inference
母集団 = ;
popu= lation
標本
sample
推論対象
調査不可能（or 困難）
知りたい（or 調査が必要）
観察対象
我々が実際に調査可能= （or 容易）な一部データ
推論
= 注意：今後特に断りのない限り，無限母集団を考える．
¡母集団が大きすぎて調査不可能な場合=
n全国大学生の身長
¡全数調査（悉皆調査）がそもそも不可= 能な場合
n品質検査
n料理の味見
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母集団と標本：統計的推論
3D"*"母集団の性質を表す数値<= /u>
3D"*"= 齦ｽ均：μ
3D"*"= 齦ｪ散：σ2（母標準偏差：σ） <= /span>
3D"*"
3D"*"母集団からの標本
3D"*"データ n 個を無作為抽出
3D"*"
3D"*"
3D"*"X1,…,Xn は互いに= 独立な確率= ﾏ数
3D"*"標本調査は試行<= /u>：無作為= 抽出により，実際に取る値は偶然による
3D"*"各確率変数 Xi は母集団= と同じ分布に従う
3D"*" n はサンプルサイズ（抽出した標本数）
3D"*"
3D"*"確率変数 X1,…,Xn から作ら= れる確率= ﾏ数
3D"*"標本平均<= span style=3D'mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti= mes New Roman"; font-size:83%;mso-fareast-hint:yes'>：
3D"*"
3D"*"標本分散<= span style=3D'mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti= mes New Roman"; font-size:83%;mso-fareast-hint:yes'>：
母集団 = ;
popu= lation
標本
sample
n 個のデータを無作為抽出した確率変数
無作為抽出には乱数などを利用 <= /div>
標本から作られる確率変数
母集団の= ｫ質を表す数値 <= /span>
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file:///C:/8ECB5C13/07dist_3.files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
標本分布：= W本平均
3D"*"= 母集団か= ら抽出した標本数 n の標本 X1,…Xn について= ，以下の確= 率変数を標本= ｽ均　 という
•注意）｢標本分散値｣は確率変数「標本分散｣が標本毎に実際に取る値
母集団 = ;
popu= lation
標本
sample
n 個のデータを無作為抽出した確率変数
標本から作られる確率変数
母集団の= ｫ質を表す数値 <= /span>
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(174,166)
(174,168)
(174,177)
(174,170)
(166,174)
：
(170,174)
(170,166)
(170,168)
(170,177)
2人ずつ
非復元抽出
母集団と標本：標本平均
3D"*"<= b>標本平均と母平均の関係
3D"*"例：5人の身長
R= 26;（170, 174, 166, 168, 177）
母集団 = ;
 population
166
168
177
170
174
標本平均の値
170.0
171.0
175.5
172.0
170.0
：
172.0
168.0
169.0
173.5
171.0
一致= ｷる！
6.0
母集団数 N=3D5
母平均 μ=3D171.0
母分散 σ2=3D16.0
標本平均値
の平均
標本平均値
の分散
<= v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelativ= e=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" stroked=3D"f">
母分散の　　　　倍（無限母集= 団）
母分散の　　　　倍（有限母集= 団）
<= /map>
Excel
標本数 n=3D2
標本
sample
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補足：標本平均の平均と母平均・標本平均の分散と母分散の関係（証明）<= /span>
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補足：有限= 齒W団修正
3D"*"母集団が有限の場合
3D"*"標本平均の分散と母分散の関係は，
3D"*"母集団が無限の場合
3D"*"標本平均の分散と母分散の関係は，
有限修正項
標本数nに比べて母集団の数<= /span>Nが大きくないとき，= L限修正項を考慮する．
無限母集団（Nが十分大きい）時は= C有限修正項は1となるので無視して良い．
Nが余り大きくない= 場合や，n/Nが大きい場合
母集団 = ;
popu= lation
標本
sample
母集団の数 N
標本数 n
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補足：母集= cと標本：標本平均
3D"*"なぜ「標本平均の分散」が「母分散」より小さくなるのか？
R= 26;　〔即ち，なぜ　　　　　　なのか？〕
3D"*"=
3D"*"例：5人の身長
= 211; （174, 166, 168, 177, 170）
「標本平均値の散らばり具合」の方が， <= /div>
「母集団= の散らばり具合」より小さい！
標= 本平均値
（各標本の標本数=3D2<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 78%;text-shadow:auto;mso-fareast-hint:yes;color:green'>）<= b>
母集団= 3;
166  167  168  169  170  171  172  173  174  175  176  177
=
分散=3D16
分散=3D6
正= 確には有限母集団なので以下
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3D"*"注意：｢標本平均｣と｢標本平均値｣は意味が= 違う
3D"*"…
3D"*"…
3D"*"｢標本平均　 = の期待値は母平均μに等しい｣
3D"*"｢標本平均　 = の分散は母分散σ2= の1/n
母集団と標本：標本平均（まとめ）
3D"*"標本平均
母集団からn<= /span>個
無作為抽出
= <= ![endif]>
有限母集団= の場合：
<= span style=3D'font-family:"Times New Roman";color:#333399;mso-color-index:5'>•X1,…,Xnはそれぞれ確率変数
•そ= れから作られる標本平均も確率変数&#= 13;
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh1AAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABADP ABoAgwAAAAAAAAkHCAoICQwKCwcGBwsKCgsJCpnMAAECAwECAwECAwECAwECAwECAwECAwT/EEiE pL046827/2AojmRpYoYwUBd7vnAsz3StEUAxWZXt/8CgJhCwEIvBAQ/QEzqf0BNSMv0dMK6odss1 AqZV2JEIGAgErWZ3zf4VkeHhO+79drLtvP4FtxvHYG8bYHdqe4dPgGQkfXQZfUN1G3iIlZYXVY4Y kJFfmkyGl6IdR1Scnp6lIap+HnCOrByUo7SdfnGcn5eztb1Uv62YwcO1vL61gsCbuJiAlsbHosnK zY/RoNfH08Tb1Ip/iuHirK/jqtDZiIuSwMzR6Ol77qn0wu+h8b661L7w+dKuSqyL9WgfCH//Eo7I 9MHgB4QKI5Jqtc+hB4gSM266BcIgmXVpLDSKFNGo2Rh2pLpNwDeypT2VtgIS68HS5UiGHXMSY8ID o81s5DqCHGSqZ48IADs= ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
= 226;１．世界に4
3D"*"4 (2, 6, 7, 5) である． <= /span>
3D"*"神様は母平均の値を求めた．いくつか？
3D"*"
= 226;２．探検家は2
3D"*"2
= 211;（つまり，非復元抽出で2
3D"*"2
3D"*" 全ての組合せについて計算せよ．
R= 11;
= 226;３．１と２の結果から， 　と 　　　が成立していること= を確認しよう．
= 226;　ただし，Nn
母= W団
演習１：標本平均
=
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R0lGODlhewAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABQBz ACUAgAAAAAAAAAL/hI+py+0Po0QhzIuz3ssCz4XiGILkeVSmaqJT654tHEN0LVYU/n687Ev9Eqyi bpgLKiXHY8R5Q3I81IzlyiRKUaAqxTjz2rRbUnfJFD9gUQ3YmTRgMeenol3OfulCvLzbxvIHF0Yl OKUixPf3kjiWMtOxI5dXeTepeEmJaVlZxznJ1tn5uckABzo6VGoqeUoEpmrWmnkX5Sc7e7NLW5v2 BhwcWysMjOZryvtllJtzq9kb3eyCB9jkiDxtiUumLcst7e2pN4L9Yb4mnhf5q15GuOi+ugQeLg/E audmeP8aVG8v3Zx+mNScY5aqUUBxZwAuPGWQoJKBFxwmkwgKFbmKDH0wHsz3ROOjcwsKAAA7 ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
母集団と標本：大数の法則
<= span style=3D'color:black;mso-color-index:1;mso-fareast-hint:yes'>3D"*"｢標本平均　 の期待値は母= ｽ均μに等しい｣
3D"*"｢標本平均　 の分散は母分= Uσ2の1/nに等しい｣
= <= ![endif]>
標本数 n が大きくなるにつ= れて，標本平均
が母平均μに近い値をとる確率は 1 に近づく．
大数の法則
n が十分大きければ母集団てもよいでしょう．=
有限母集団= の場合　　　　　倍
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R0lGODlhTQAsAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABQBG ACQAgAAAAAAAAAKlhI+py+0dwpu0WiNBvrzf7YWiAo6mV55qJaXrGsVy/NbY5tpvmesqb5vJTqme b1R0DDW0Ay9ya4agtwmI6lxcs6KlFQHUcsdHMBnDyCTLCVxbmTPuzholpC2UU9TidE//U9dHgjbI koc4I0jIuPgGlkf01+hoxlZ4F6UmhXn5xQHo2fkpymJaipqqusrairLpOlUXGos3WmvFh/tBt5s5 67vnlFMAADs= ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
母集団と標本：大数の法則
3D"*"大数の法則
3D"*"例：サイコロを振って出= た目の平均〔μ=3D3.5
Excel
標本平均が= 母平均〔μ=3D3.5〕に漸近する様子
小　←　標= 本数　→　大
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R0lGODlhPAAgAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA6 AB4AgQAAAJnMAP///wECAwKehI+pyxsNo5wmPIozDOLq/3EdSGLiWKbNiaruwbaKBVh0bef6zvfC D/QgOA9REYhMKpdMprAyMtaa1Kr1SZxGrdwuUpiVxrxkJ2yLLqvN02N6Df+2te64/WdB1+/xvHvP p3b0pxUoCEU4Znh1lrhIBqZX+FiFJalImfRUUWTD2QMaqqO0+QISU2oaIqfqcpLaqiEV6ypDW3Jz qwKbUAAAOw== ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
補足：大数= ﾌ法則
大数の法則
3D"*"証明はチェビシェフの不等式 から
∵） X1,…,<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>X<= /span>n は独立で，= 同じ分布に従う
→<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-special-format: lastCR;display:none'>
とすると
ここで，チ= ェビシェフの不等式から，kσ:=3Dεとおくと　（σ2:=3Dσ<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:67%;position:relative; top:-.45em;mso-text-raise:30%;mso-fareast-language:JA'>2/n= ）
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= 母平均μ，母分散σ2の母集団から大きさ n の標本を無作為に抽出した時，= n = が十分大きければ，母集団の従う= 確率分布に関係なく，標本平均 　は平均μ，分散σ2 /n の正規分布 N(μ,σ2/n ) に従うとみなすことができる
標本分布
3D"*"標本平均　 はどんな確率分布に従うのか？
3D"*"<= ![endif]> = ;
3D"*"母集団分布が正規分布 N(,2 ) の場合〔母平均μ母分= Uσ2〕 <= /span>
= 211; 標本平均　<= span style=3D'font-size:83%;color:black;mso-color-index:1'> は正規分布 N(μ,= σ2/n ) に従う
3D"*"<= ![endif]> = ;
3D"*"母集団分布が正規分布ではない場合〔母平均μ母分散σ2〕 <= /span>
= 211; 標本平均　<= span style=3D'font-size:83%;color:black;mso-color-index:1'> は正規分布 N(μ,= σ2/n ) に従う
<= ![endif]> =
中心極限定理
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データ分布と予測　3．母集団と標本
= ;
中心極限定理
母集団 = ;
popu= lation
標本
sample
= 母平均= 3;
母分散
= 標本平均= 3;
標本分散
標本平均
一様分布
二項分布
ポアソン分布
正規分布
幾何分布
指数分布
標本数 n が十分大きいなら
n個とってくる<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";color:#3333FF; mso-special-format:lastCR;display:none'>
…
中心極限定理は，母集団分布がなんであっても（正規分布でなくても），標本数= n が十分大きければ，標本平均 X は，近似的に正規分布 に従う，と述べている =
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Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
= ;
中心極限定理
母集団 = ;
popu= lation
標本
sample
母平均= 3;
母分散
標本平均= 3;
標本分散
標本が十分大きいならば
n個とってくる
サイコロを100回投げる
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0a3udn+I3e6Od3PgLe96o4Xe6vuJQr397Xzru9/OSTC+9VkWgBOcJAan6783MvCcIvzeCG94wjNq 7IQfnN88Ae4ciWbxgcuq4faebMgrPnJ9Z7PkCi5H+cNVXiKLjxzk53a5vSnO8pTWvOKalHm4YX5z lPO85y/XOdCDnu2iG/3okAsIADs= ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
　　　　　のとき，
が成りたつ．言い換えると，
としてよいということ．
（右辺のφは標準正規分布の累積分布関数)
補足：中心= ﾉ限定理
中心極限定理
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5UcUQRrnZNgHOkdSnC7ESYOrPgQGNbu+ggmfy/5BBAA7 ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0054.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
中心極限定理の応用
3D"*"例題： 40,000回投げるとき，表が20,400回より多いか，19,600 <= /div>
平均20,000回で，
400回は±2％の誤差！
ありふれたことだろう．．．
二項分布 Bi(40000, 1/2) に従う
<= span style=3D'font-family:"Times New Roman";font-size:71%'>3D"*"i Xi=3D1,0 10
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >3D"*"<= span style=3D'mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti= mes New Roman"; font-size:71%;mso-fareast-hint:yes'>表の出る回数：X=3DX1+X2+…+Xn
を計算すれ= ばよい！
ところが 40000Cxを計算するのは困難！
例えば，Excel2003= で40000C19600を計算すると，…
計算不能！
つまり P( X > 20400 ) + <= /span>P( X < 19600 ) はいくつか? =
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中心極限定理の応用
3D=nが十分大きければ，二= 項分布は正規分布で近似できる！ <= /div>
各Xi は二項分布 Bi(1, 1/2) に従う
μ=3D E( Xi  ) =3D ni pi =3D 1×1/2 =3D 1/2,
σ2=  =3D V( Xi  ) =3D ni pi (1 - pi) =3D 1×1/2×1/2 =3D 1/4
故に，求める確率は 1%未満．殆ど起こりえないこと！
=
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中心極限定理の応用
3D"*"= 標準正規= 分布表の読み方
小数第１位
小数第２位
N(0,1)
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標本分布：= W準化と標準正規分布
3D"*"例題：
–　確率変数 X はある株式の利回り(%)で，正規分布N(3,10= )に従う．= = この株式= への投資が損となる確率は？
標準正規分布表から
＝0.171391 (Excel関数 NORMDISTより）
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<= span style=3D'font-family:"Times New Roman";font-size:86%;color:black;mso-color= -index: 1;mso-fareast-hint:yes'>3D"*"平均μ，分散σ<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:57%;mso-fareast-hint:yes; color:black;mso-color-index:1;position:relative;top:-.45em;mso-text-raise: 30%;mso-fareast-language:JA'>2 /nの標本平均　の標準化=
標本分布：= W本平均の標準化
3D"*"= 平均μ，= 分散σ2の確率変数 X の標準化=
= =
標本から母平均μを= 定
「Z推定」・「Z検定」
に利用する
標本平均が，正規分布 N<= /span>（μ,σ2= /n= ）に従うとき，標準化した確率変数 Z は，標準正規分布 N（0, 1）に従う
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
例題：出展 技術評論社「確率・統計の仕組みがわかる本」 例7.2
3D"*"<= span style=3D'font-size:63%;mso-fareast-hint:yes'>解答：母集団分布不明だが，n=3D36人は十= 分大きいので，中心極限定理から正規分布と仮定．標本平均　= @の分布は
• 平均：2250円（母集団と同じ），標準偏差= F
• の正規分布に従う．これより標= 化して，
【問題】小学生の1ヶ月の小遣いが，平均2250円，標準偏= 差360円です．このとき，ランダムに= 選んだ36人の小学生の小遣い平均が2400円を超える= 確率は？
=
•したがって
•∴ 答え 0.62%
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Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
Coffee Break!
= 101= 00と1001= 0はどっちが大きい<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:91%;color:#006600; mso-fareast-language:JA'>?
3D"*"= どちらが大きい？
3D"*"101= 00 ＝ ?
3D"*"10= 01= 0 ＝ ?
&= #13;
3D"*"どちらが大きい？ <= /span>
<= span style=3D'font-family:"Times New Roman";font-size:71%;color:#006600;mso-far= east-hint: yes'>3D"*"101= 00 ＝ ?
<= span style=3D'font-family:"Times New Roman";font-size:71%;color:#006600'>3D"*"100! ＝ ?
&= #13;
3D"*"スターリングの公式
充分大きなNにつ<= /span>= いて，Nの階乗の= 近似値を与える
累乗の計算も大変だけど，階乗の計算はとんでもなく大変ね!
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標本分布：= W本分散
3D"*"= 母集団か= ら抽出した標本数 n の標本 X1,…Xn について= ，以下の確= 率変数を標本= ｪ散 S2という
•注意）｢標本分散値｣は確率変数「標本分散｣が標本毎に実際に取る値
母集団 = ;
popu= lation
標本
sample
n 個のデータを無作為抽出した確率変数
標本から作られる確率変数
母集団の= ｫ質を表す数値 <= /span>
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file:///C:/8ECB5C13/07dist_3.files/slide0014_image296.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhQAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABgA6 AA4AgAAAAAAAAAJUhIOHYe0PI1wqRdaw3Pw6LWFgR3YiyYzl6qmXy8bKatFaXW+5DsDhDTT1UIfH TsYbcm4TJLH4SyxAIp+OSplmUiUm0voCQ8UeGffpdJ5Nx3S3FygAADs= ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0062.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
(174,166)
(174,168)
(174,177)
(174,170)
(166,174)
：
(170,174)
(170,166)
(170,168)
(170,177)
2人ずつ
非復元抽出
母集団と標本：標本分散値の平均
3D"*"= 母分散と標本分散の関係=
3D"*"<= span style=3D'font-size:83%;mso-fareast-hint:yes'>例：5人の身長
母集団 = ;
 population
166
168
177
170
174
標本分散値
16.0
9.0
2.3
4.0
16.0
：
4.0
4.0
1.0
12.3
10.0=
標= 本
sample
母集団数 N=3D5
母平均 μ=3D171.0
母分散 σ2=3D16.0
標本分散値
の平均
母分散の　　　　倍（無限母集= 団）
母分散の　　　　倍（有限母集= 団）
<= /map>
Excel
標本数 n=3D2
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補足：標本分散の平均と母分散の関係（証明）
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補足：有限= 齒W団修正
3D"*"= 母集団が有限の場合
3D"*"= 標本分散の平均と母分散の関係= ﾍ，
3D"*"
3D"*"
3D"*"
3D"*"
3D"*"
3D"*"= 母集団が無限の場合
3D"*"= 標本分散の平均と母分散の関係= ﾍ，
有限修正項
母集団の要素数Nが大きくないとき，= L限修正項を考慮．
無限母集団（Nが十分大きい）時は= C有限修正項は1となるので無視．
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3D"*"注意：｢標本平均の分散 = 　　｣と｢標本分散の平均 　　｣を混同しないこと！
母集団と標本：標本分散（まとめ）
3D"*"標本分散 S2
有限母集団= の場合：
｢標本分散= 値の平均｣と「母分散」の関係
母集団からn<= /span>個
無作為抽出
•<= /span>X1,…,Xnはそれぞれ確率変数
•そ= れから作られる標本平均も確率変数
<= span style=3D'font-family:"Times New Roman";color:#333399;mso-color-index:5; mso-fareast-hint:yes'>•よ= って，それから作られる標本分散も確率変数&#= 13;
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Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
= 226;１．世界に4
3D"*"4 (2, 6, 7, 5) である． <= /span>
3D"*"神様は母分散の値を求めた．いくつか？
3D"*"=
= 226;２．探検家は2
3D"*"2
= 211;（つまり，非復元抽出で2
3D"*"2
3D"*" 全ての組合せについて計算せよ．
R= 11;
= 226;３．１と２の結果から， 　 = 　　　が成立することを確認しよ<= /span>う．
= 226;　ただし，Nn
母= W団
演習２：標本分散
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ACAAgAAAAAAAAAL/hI+py+0eIorh2asq3rz7pR3hR0rkiabVOKZc68YyCIRwJ1HbPffxKnIBeTSf UWYzEDHAmoiimxxxS2SwejFhpdSZZotKgiHBHU7pG39appPYvGbKnek2Pfzc2eE1KCsRlVQ2RViI xnXHlof2Z+iYlsg4eHgIhfiIGRZF13hpoZbp6Lf3ZHdDygAaStiZQfkKmDUxuorZGnsHe1ukN+r7 C3wJPPzrSdSpOJk661crius6ydKGpercMw1Ci/iFCn3t3FziBl5u5WFtrv4tqzk9lr5enpwVLx+e q2Z/v9qU2+5mhTd+PyK9EOJkH8FllQBtU4aO00Ijb85ogjWxoCSLFOQwZsQzK2LHhB9/mEI38NOi GQUAADs= ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0048.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
標本分布：= W本分散と不偏分散
3D"*"標本分散 S2= 3;
3D"*"不偏分散 s2
この標本分散は，母分散σ2= の不偏推定量
有限母集団= の場合：
N<= /span>が充分大きいならば，
N<= /span>/(= N<= /span>-1)は1と考えて良い．
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標本分布：= W本分散の従う確率分布
3D"*"標本分散S2 はどんな確率分布に従うのか？
3D"*"母集団が正規分布 N(μ,σ2 ) に従うとみなせる時，= 確率変数　　 自由度<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:86%;text-shadow:auto; mso-fareast-language:JA'>n-1のχ<= u>2 (n-1)分布に従う．
…
n個のN<= /span>(0,1)に従う確率変数の二乗和
χ2分布に従う
という制限の= ため，自由に動ける変数の個数はn-1となる．
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χ2 分布とは？
3D"*"= 標準正規分布 N(0,1) な n Z1,…,Zn
二乗和をと= る
新たな確率= 変数
この確率変数χは，自由度n のχ<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:67%;mso-fareast-hint:yes; position:relative;top:-.45em;mso-text-raise:30%;mso-fareast-language:JA'>2= 分布に従う！
互いに自由に値をとることが出来る確率変数の個数
n=3D1
n=3D2
n=3D3
n=3D4
n=3D5
n=3D6
χ2(n)
N(0,1)
標本から母分散σ2を推定 = ;
「カイ二乗推定」「カイ二乗検定」 =
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file:///C:/8ECB5C13/07dist_3.files/slide0052.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
標本分布：= W本分散
3D"*"= 例題：ある正規母集団の母平均μ=3D50,2=3D25とする．ここから大きさ1050える確率は？
自由度9のχ2= 分布表から
P(χ2(9)>19= .0228 )=3D0.025
P(χ2(9)>21= .6660 )=3D0.010
= ＝0.017912
 (Excel関数 CHIDISTより）
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ギネスビールと= ﾍ？
1756= N創業のビール醸造会社
〔ダブリン（アイルラ= 塔h）〕
ギネスビール（黒スタウト）を製造
t<= /span> 分布とは？
3D"*"= 2個の互いに独立な確率= 変数 X, Y を考える． <= /span>
3D"*"X 標準正規分布 N(0,1)
3D"*"Y 自由度 n のχ2分布 χ2= (n) に従う
新たな確率変数
=
確率変数<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> T = は，自由度 n の t = 分布に従う！
X〜N(0,1)
Student の t<= /span>分布
ゴセット (1876-1937)
Y〜χ2(n)
T<= /span>〜t (n<= /span>)<= /div>
ビール会社ギネスGuinessでビールの品質管理
標本が小さいとき，分散の値が(…
　→　t 分布の発見（<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:89%;mso-fareast-hint:yes; color:black;mso-fareast-language:JA'>"Student"[W.S.Gossett] ‘The proba= ble error of a mean’,Biometrika vol.6,1908）
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標本分布：= W本平均と標本分散
3D"*"標本平均　　の標準化
=
3D"*"標本分散S2= に　　を掛けた<= span style=3D'position:absolute;top:33.75%;left:52.62%;width:44.56%;height:4.75= %'>確率変数
=
標準正規分布N(0, 1) に従う
自由度 n-1 のχ2分布 に従う
標本から母平均μを= 定
「t推定」「t検定」
自由度<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman";text-shadow:auto;color:#9900CC'> n-1 の
t 分布 に従う
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Content-Location: file:///C:/8ECB5C13/07dist_3.files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
演習３：
3D"*"= 2006= N晩秋ゲーム機商戦たけなわ，ゾニーのPlayState3と任天童のViiが発売された．ゲーム機を購入に来た客10= 人に聞いたところ，次のような結果を得た．= = iただし，必ずどちらかを購入し，どちらも買わない客はいないとする）この<= span style=3D'mso-hansi-font-family:Arial;font-size:56%;mso-fareast-hint:yes'>= ﾆき，PS3を購入する比率（標本比率）を計算せよ．
•PS3= @PS3　Vii　PS3= @Vii　Vii　Vii= @PS3　Vii　Vii=
•
3D"*"昨シーズン打率28し，4503この打者が，確率0.23<= span style=3D'mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti= mes New Roman"; font-size:56%;mso-fareast-hint:yes'>ればならないか？
•(出展：「統計学入門」東京大学出版会 p.173 8.3)
のとき，
だが，計算は大変だし，nが未知
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本
補足：必要な= 標本の大きさ
3D"*"標本平均の実現値を母平均の推= 闥lとする場合
=
誤差
許容誤差
　定められた許容誤差ε>0に対し，母集団の大きさNと母標準偏差= σが既知の場合，単純無作為抽出の大きさnを，左不等式を満たすようにとれば= ，95%以上の確率で，誤差を許容= 誤差より小さくできる．
今，標本平均の従う正規分布から考えて
従って，許容誤差をεとしたとき
95％
-1.96
1.96
参考：
有限母集団の場合
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補足：必要な= 標本の大きさ
3D"*"例題：6000p95誤差が0.05出の大きさnはいくらか？
Nが十分大きいので，<= /span>
σ2の最大値は0.= 25(p=3D0.5の時）
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参考文献
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l東京大学教養学部統計学教室編「自然科学の統計学」東京大学出版= = （1992）
<= span style=3D'font-family:"ＭＳ Ｐゴシック";font-size:63%;color:black;mso-farea= st-hint:yes'>l鈴木達三・高橋宏一「標本抽= 出の計画と方法」放送大学（19= 91）
<= span style=3D'font-family:"ＭＳ Ｐゴシック";font-size:63%;color:black;mso-farea= st-hint:yes'>l永田靖「サンプルサイズの決= め方」朝倉書店（2003）
<= span style=3D'font-family:"ＭＳ Ｐゴシック";font-size:63%;color:black;mso-farea= st-hint:yes'>l白石修二「例題で学ぶ Excel統計入門」森北出版（2001）
<= span style=3D'font-family:"ＭＳ Ｐゴシック";font-size:63%;color:black;mso-farea= st-hint:yes'>l村上雅人「なるほど統計学」海鳴社（2002<= span style=3D'mso-ascii-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Ｍ= Ｓ Ｐゴシック"; font-size:63%;mso-fareast-hint:yes;color:black'>）
<= span style=3D'font-family:"ＭＳ Ｐゴシック";font-size:63%;color:black;mso-farea= st-hint:yes'>l丹慶勝市「図解雑学 統計解析」ナツメ社（2003）
l高橋信[著]・トレンドプロ[マンガ]「マンガでわかる統計学」オ= ーム社（2004）
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if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } var g_HLinkArray =3D new Array(); =20 function IMapAreaObj( areaObj, coords ) { this.areaObj =3D areaObj; this.coords =3D coords; } function InitHLinkArray() { var appVer =3D navigator.appVersion; var msie =3D appVer.indexOf ( "MSIE " ) var ver =3D 0; if ( msie >=3D 0 ) ver =3D parseInt ( appVer.substring( msie+5 ) ); linkNum =3D 0; for (i=3D0; i 4 ) ) g_HLinkArray[linkNum++] =3D new IMapAreaObj( areaObj, ParseCoords( ar= eaObj.coords ) ); } } function ScaleHyperlinks( factor ) { =20 for ( ii=3D0; ii< g_HLinkArray.length; ii++) { coordsStr=3D""; imaObj =3D g_HLinkArray[ii]; for ( jj=3D0; jj < imaObj.coords.length-1; jj++ ) coordsStr +=3D (imaObj.coords[jj]*factor) + ","; coordsStr +=3D (imaObj.coords[jj]*factor); imaObj.areaObj.coords =3D coordsStr; } } function ParseCoords( coordsStr ) { var numArray =3D new Array(); var i =3D curPos =3D commaPos =3D 0; while ( ( commaPos =3D coordsStr.indexOf(",", curPos) ) !=3D -1 ) {=20 numArray[i++] =3D parseInt( coordsStr.substr( curPos, commaPos ) ); curPos =3D commaPos + 1; } numArray[i] =3D parseInt( coordsStr.substr( curPos ) ); return numArray; } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"スライド ショーの最後です。 クリックすると終了します。"= , SCREEN_MODE=3D"Frames", gIsEndShow=3D0, NUM_VIS_SLDS=3D41, SCRIPT_HREF=3D= "script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0043.htm",1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("= slide0024.htm",1,-1,1),new hrefList("slide0069.htm",1,-1,1),new hrefList("s= lide0041.htm",1,-1,1),new hrefList("slide0061.htm",1,-1,1),new hrefList("sl= ide0057.htm",1,-1,1),new hrefList("slide0037.htm",1,-1,1),new hrefList("sli= de0002.htm",1,-1,1),new hrefList("slide0040.htm",1,-1,1),new hrefList("slid= e0004.htm",1,-1,1),new hrefList("slide0060.htm",1,-1,1),new hrefList("slide= 0005.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("slide0= 038.htm",1,-1,1),new hrefList("slide0067.htm",1,-1,1),new hrefList("slide00= 10.htm",1,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide005= 5.htm",1,-1,1),new hrefList("slide0056.htm",1,-1,1),new hrefList("slide0053= .htm",1,-1,1),new hrefList("slide0011.htm",1,-1,1),new hrefList("slide0025.= htm",1,-1,1),new hrefList("slide0066.htm",1,-1,1),new hrefList("slide0014.h= tm",1,-1,1),new hrefList("slide0062.htm",1,-1,1),new hrefList("slide0063.ht= m",1,-1,1),new hrefList("slide0064.htm",1,-1,1),new hrefList("slide0065.htm= ",1,-1,1),new hrefList("slide0068.htm",1,-1,1),new hrefList("slide0048.htm"= ,1,-1,1),new hrefList("slide0015.htm",1,-1,1),new hrefList("slide0045.htm",= 1,-1,1),new hrefList("slide0052.htm",1,-1,1),new hrefList("slide0046.htm",1= ,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("slide0047.htm",1,= -1,1),new hrefList("slide0058.htm",1,-1,1),new hrefList("slide0059.htm",1,-= 1,1),new hrefList("slide0030.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"次へ",sPrev=3D"前へ",sEnd=3D"スライド ショーの終了",sFont=3D"= lＳ 明朝",sArrow=3D"矢印",sFreeform=3D"フリーフォーム",sRect=3D"四角形",sOv= al=3D"楕円" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; s.fontFamily=3DsFont s.fontSize=3D"9pt" s.paddingLeft=3D2 } function CreateSeparator( node ) { var sObj=3DCreateItem( node ) SetCMBorder(sObj,"menu","menu") var s=3DsObj.style s.borderTopColor=3D"threedshadow" s.borderBottomColor=3D"threedhighlight" s.height=3D1 s.fontSize=3D"0px" } function CreateItem( node ) { var elem=3DPPTSld.document.createElement("DIV") node.insertBefore( elem ) return elem } function SetCMBorder( o,ltClr,rbClr ) { var s=3Do.style s.backgroundColor=3D"menu" s.borderStyle=3D"solid" s.borderWidth=3D1 s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr } ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/fullscreen.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/buttons.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhWAESAPf4AAAAAIAAAACAAICAAAAAgIAAgACAgICAgAQEBISEBASEBISEhAQEhMTExAQE /KTM9Pz8/ERERPz8BAT8/KSkpGRkhMTcxCRkxAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAMDAwP8AAAD/AP//AAAA//8A/wD//////yH5BAEAAPgALAAAAABYARIA QAj/APEJHEiwoMGDCBMqXMiwocOHECNKnEixosWLGCEiQKCRo8YDIEHig2DxAD4LKD1avDDhgUuV GUOGbHBR5QGYFBG4fHAB58EKECJEwCfUYAWPFGAygLCRKQIIUKM6WAohKUGgCikcFWh1INWoYKVS 7SrQ41GbIhGYLAuVQVOoC+IyXUuUAkG1HE3KFDhAwkgJc5/qDZmxsOHDiBMrXsy4sePDGyP7lChT 5MULmDPnlDw5YmW6FTNrfgi0aNGEZPEtbfo2bNTUpYeeRph69dPWrqvCNFuBIGG1A59CYPAVQtwF cw0OxWdTIOiBCQAjaAB17fOFII8voGmRc+eOkilm/z9OvTtnjN4hYk1YoT3H2rnBOphPAB9skgq3 2lcaX/5YnJVt9BloAar12UEIRGCZdQghMABI1Tn32IQUVthYexhmqGGGMBHAgIfEhSiiiATAtOGJ GnYI4ogsEldicAYOGNJGZaml3Y0L3NTZUBz1xlB0PUoUI0jlVWRSVN89xBKSGB1YU1TMoRfVBEle hR9HQs1GEHxQ3RZZbveZthxt/LEmXHyp5XWABSCpaRJwbM13gAACPHVccgJFgF+NEhqUAEkQSCfc ddhVhh5dVTaEAEsTUNlkZUWKN9BNGDE6QU8OrSdbllzpxyVTTrU21Uj3scfhp7nNpyoDaTIEJ3P9 If8J2kbLNYegg9JRBwGhFvbq66+ZUiDssMQWK2yHxiZLrInKNotss8l+B5yBrr5p2UIJvortANoC 6+234IbLla/elRtZjeamh5CC3Sb0YLvixivvYkDFGlZqBNh7r4n6goVvv6/ZlCicN+kL71ALTnpQ dCIZp7CihkLA3UQmoWRBogyxtBPGCTnZncVR1rSTo5nuydC/Eo8kUH+lOoTyyvjoCuZu+PjYIKLD rZybtrM1d10C0QXKEVz48GrQkEeWdFJKlbb0UmEeV0SzyC6RvNB646LWIVjUNeC1zAFb+RDKXksM 9r531bwmpQW9+hQDDsx5pqwDRWBXcFES2hc+gEn/wJGdEEWdE6LoWcoxQweaTNmkhydkKaYMYY2Q p1unbLl/pPKbn3v7EZRvrKvqlja2ONvrtoIw9tn2g32/tQBlhtYkU+MNikZ7QYlPDPuMldpOmuJX nVo5VF3HjI+q89mteX5IDd/fVFClma5kiE4f2XUJhlz09gj2NbTDRifkmu7zXjR++RVJ/lPznuvr QH2iD6S+UewP9Dnon6d2NLwN8n90BB6hC68cFMCHoe+ACASP9c4DowUyEF0OPFcDI0ij/VXPaAKC UfhS95AKGoQ7IBRICI1HwhGaUIQoLGEKT6jCFrLwhSuMoQtlCMMZ2rCGOKShDm+4wxzy8Ic+DGIP B4cIRCKGMCAAOy== ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/frame.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　3．母集団と標本 ------=_NextPart_01C82EB7.CB84CCB0 Content-Location: file:///C:/8ECB5C13/07dist_3.files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
 ノ= ート
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アウトライン
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