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1 2 Web Multivariate/index.html
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3 : RAND() (.xlsx) RAND() 2.1 Microsoft Excel 2007 Sheet1 RAND().xlsx Excel Excel URL( B3 = RAND() (2.1)
4 RAND Enter RAND() B RAND() (1) B3 Shift B12 (2) (3) (4) (5) RAND() F9 F9 2.2: RAND() (.xlsx) RAND() x 0 < x < 1 (0, 1) 0 x 1 [0, 1] 0 < x 1 (0, 1] RAND() (0, 1) 27
5 : 2.4: (.xlsx) RAND() =17 15 RAND() [1] Excel Excel VBA(Visual Basic for Application) Excel VBA???? IX, IY, IZ [1, 30268], [1, 30306], [1, 30322]
6 4 2 IX = MOD(171 IX, 30269) (2.2) IY = MOD(172 IY, 30307) (2.3) IZ = MOD(170 IZ, 30323) (2.4) RAN DOM = MOD(IX/ IY/ IZ/30323, 1) (2.5) 30269, 30307, MOD(I, J) I J (2.2) Excel B B6 (2.2) B5 B B B D 2.6 IX B5 Shift Ctrl (2) (3) (7) IX (4) D5 IX 2.5 E D E5 E30271 D G5 E IX (2.3) (2.4) , IX, IY, IZ 3 7 [2] , 30306, (= ) (2.5) IX, IY, IZ 1 IX/30269, IY/30307, IZ/ < IX/ IY/ IZ/30323 < 3 (2.6)
7 : RAND() IX (IX.xlsx) 2.6: IX (0, 3) 27 IX/ IY/ IZ/ (0, 1), (1, 2), (2, 3) (0, 1) x, y a, b, c, d 0 < a, c < x, 0 < b, d < y a x + b y = 1 + c x + d y (2.7)
8 6 2 c/x + d/y a/x + b/y 1 (b d) x y = x (a c) (2.8) x, y b d < y 0 0 (2.5) RANDOM (0, 1) (a) (2.2) (2.4) IX/30269+IY/30307+IZ/30323 (0, 3] (0, ], (0.0001, ] IX/ IY/ IZ/30323 (0, 1], (1, 2], (2, 3] 3 (0, 1] 2.7 (b) (2.5) RANDOM RAND() (0, 1) 7 1 RAND() 2.8 (2.5) RANDOM (2.2) (2.5) i R 1i R 1i R 1i = 1 nv 2 e n (r 1j r)(r ij r) (2.9) j=1 r ij i j r, v 2 e n = 1000 v 2 e v 2 e = 1 n 2 1 n i=1 n (r ij r) 2 (2.10) RAND() j=1 Excel RAND() 2.1, 2.2 RAND() Excel RAND() (2.2) (2.4) IX, IY, IZ RAND() Excel =RAND() (0, 1)
9 : RAND() 2.8: RAND() RAND() 1000 B4 D4 1 IF(a, b, c) a b c B7 A IF A7 [0.0101, ] A % [0.925, 1.053] Excel RAND()
10 :.xlsx 2.10: ( p p 1 6 {2, 4, 6}
11 2.2. ( RAND() RAND() 0 1 RAND() 2.11 B7 B16 = INT(2 RAND()) (2.11) 2 RAND() (0, 2) INT() 1 0 B7 B16 10 B4 = COUNT(B7 : B16) (2.12) B7 B16 C19 = COUNTIF($B$7 : $B$16, B19)/$B$4 (2.13) B7 B16 B19 B7, B16, B4 $B$7 $B$16 $B$4 $ (2.13) C20 B7, B16, B4 B19 $ (2.13) B19 B20 C (1) (2) (3) (4)2-D (1) (2) (3) ( B19 B20 (4)(5) 2.11
12 : (n=10)( n=10.xlsx) 2.12: (n=10)
13 2.2. ( : (n=10) 2.14: (n=10) B7 B16 INT(2*RAND()) B7 B1006 B4 COUNT(B7:B16) COUNT(B7:B1006) n
14 12 2 F19, F : (n=1000)( n=1000.xlsx) 2.16: (n=1000) Excel 1 6 1/6 2.19
15 2.2. ( : (n=1000) 2.18: (n=1000) = INT(6 RAND()) + 1 (2.14) 6*RAND() (0, 6) INT() B7 B5006 B4 F19 F /6
16 : (n=5000)( n=5000.xlsx) f(x) = 1 2πσ exp ( ) (x µ)2 2σ 2 (2.15) µ σ µ = 0, σ = 1 f(x) = 1 ) exp ( x2 2π 2 F (x) f() F (x) = x (2.16) f(y)dy (2.17) 2.20 x B4 x -4 B5 = ROUND(B , 1) (2.18)
17 2.2. ( 15 ROUND(a, b) a b+1 B (10) = (2) (2.19) (i) i (2) = (10) = (10) (2.20) (10) 2.20: (.xlsx) 2.20 C4 = NORMDIST(B4, 0, 1, FALSE) (2.21) NORMDIST(a, b, c, d) d FALSE b, c x = a b = 0, c = 1 (2.21) B4
18 : 2.22: 2.21 (1) (2) (3) (4) NORMDIST(x, 0, 1,TRUE) 2.22
19 2.2. ( 17 (2.17) F (x) f(x) (a) x = 1.81 x x = 1.81 (b) F (x) : (n=5000) n=5000.xlsx 2.23 = NORMSINV(RAND()) (2.22)
20 18 2 NORMSINV() RAND() (0, 1) 2.24 RAND() F (x) NORMSINV() x RAND() (0, 1) 0.5 RAND() NORMSINV() 0 0 x RAND() 0 1 NORMSINV() x 2.24: 2.23 = ROUND(NORMSINV(RAND()), 0) (2.23)
21 2.2. ( G19 = NORMSDIST(E ) NORMSDIST(E19 0.5) (2.24) 3 ± 0.5 NORMSDIST(x) x G (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) 2.25 Excel.xlsx 2.25:.xlsx
22 : 2.27: 2.3 ( x n n q x = q/n n
23 2.3. ( Excel 2.28 n = 2 q q/n 1 i q i x i = q i /n 2.28 N = 5000 x i, i = 1, 2,, N x i AVERAGE() B10 AVERAGE(B7:B8) B7, B8 i j x ij i x i n x i = 1 n j=1 x ij (2.25) B x x x = 1 N N x i (2.26) i=1 C12 ve 2 VAR(B10:GJI10) v 2 e v 2 e = 1 N 1 N (x i x) 2 (2.27) i= C15 B10 BJI B15 (=0) C4 (=5000) 0 NORMDIST(x, µ, σ,true) (2.17) f() (2.15) µ, σ B12, C x ve 2 ve 2 NORMDIST(x , x, ve,true)-normdist(x , x, ve,true) 2 x ± 0.25 TRUE NORMDIST(x, µ, σ,true) x FALSE x 2.30 x i = 0 1 x i = 0.5
24 :, n=2 n=2.xlsx 2.29: /, n=2 n=2.xlsx 2.30: / n=2 n n= x i n=10
25 2.3. ( :, n=10 n=10.xlsx 2.32: /, n=10 n=10.xlsx f(x) = λe λx (x 0) (2.28)
26 : / n=10 [0, x] F (x) F (x) = x λe λx 0 = [ e λx] x 0 = 1 e λx (2.29) 2.24 F (x) RAND() (0, 1) F (x) RAND() = 1 e λx (2.30) x = 1 ln(1 RAND()) (2.31) λ 1-RAND() (0, 1) RAND() (0, 1) x = 1 ln(rand()) (2.32) λ 2.34 B7 (2.32) B4 λ = 2 B C14 B9 GJI [0, 0.1) n=
27 2.3. ( :.xlsx 2.35:, n=10.xlsx 2.36: n= n=
28 :, n=4 n=4.xlsx 2.38: /, n=4 n=4.xlsx 2.39: / n=4
29 : / n=100 n=100.xlsx 2.4 x i, i = 1, 2,, n ve 2 s2 ve 2 1 n = (x i x) 2 n 1 i=1 s 2 = 1 n (x i x) 2 (2.33) n i=1 ve 2 s2 n 1 n Excel VAR() (2.27) ve 2 s B9 B18 µ = 0 σ 2 = 4 10 µ = 0 σ 2 = 4 B9 B18 C9 C18 µ = 0 x i 2 (x i µ) 2 B20 C9 C18 B21 B22
30 B24 C26 σ 2 = 4 B :.xlsx 2.42:
31 29 [1] B. A. Wichmann and I. D. Hill, Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 31, No. 2, pp , [2] B. A. Wichmann and I. D. Hill, Correction: Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 33, No. 1, p. 123, 1984.
32 30 (0, 1), 2 [0, 1], 2 2, 15 AVERAGE(), 21 COUNTIF(), 9 COUNT(), 9 Excel VBA, 3 INT(), 9 NORMDIST(), 15, 16, 21 NORMSDIST(), 19 NORMSINV(), 18 RAND(), 1 RAND(), 4 ROUND(), 15 VAR(), 21, 2, 2, 14, 18, 14, 2, 18, 2, 2, 8, 10, 9, 12, 1, 2, 8, 6, 8, 15, 8, 14, 27, 1, 8, 12, 2, 21, 8, 2 $, 9, 2, 19, 14, 18, 17, 14, 27, 27
33 31, 6, 21, 27, 21, 14, 21, 9, 19, 27, 27, 27, 3, 15, 2, 9, 2, 2
34 32 3, Web
( 28 ) ( ) ( ) 0 This note is c 2016, 2017 by Setsuo Taniguchi. It may be used for personal or classroom purposes, but not for commercial purp
( 28) ( ) ( 28 9 22 ) 0 This ote is c 2016, 2017 by Setsuo Taiguchi. It may be used for persoal or classroom purposes, but ot for commercial purposes. i (http://www.stat.go.jp/teacher/c2epi1.htm ) = statistics
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Excel97 SUM Microsoft Excel 97... 1... 1... 1... 2... 3... 3... 4... 5... 6... 6... 7 SUM... 8... 11 Microsoft Excel 97 AVERAGE MIN MAX SUM IF 2 RANK TODAY ROUND COUNT INT VLOOKUP 1/15 Excel A B C A B
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\n Title 情 報 教 育 におけるグループ 課 題 の 試 み Author(s) 五 月 女, 仁 子, Soutome, Hiroko Citation 商 経 論 叢, 48(3): 1-12 Date 2013-03-20 Type Departmental Bulletin Paper Rights publisher KANAGAWA University Repository
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Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009631 このサンプルページの内容は, 初版 1 刷発行時のものです. Excel URL http://www.morikita.co.jp/books/mid/009631 i Microsoft Windows
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\n Title Excel 実 技 試 験 の 採 点 プログラムの 実 施 について Author(s) 五 月 女, 仁 子 ; Soutome, Hiroko Citation 商 経 論 叢, 46(3): 13-24 Date 2011-02-28 Type Departmental Bulletin Paper Rights publisher KANAGAWA University
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