t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1"

Transcription

1 t χ F Q t χ F µ, σ N(µ, σ ) f(x µ, σ ) = ( exp (x ) µ) πσ σ 0, N(0, ) (00 α) z(α) t χ *. t (i)x N(µ, σ ) x µ σ N(0, ) (ii)x,, x N(µ, σ ) x = x+ +x N(µ, σ ) (iii) (i),(ii) z = x µ N(0, ) σ N(0, ) ( N(0, ), N(9, 4) N(0, ) * 733 de Moivre 00

2 (iii) x, x N(µ, σ ) () z = x µ N(0, ) () σ 3 t t t Studet( Gosset: ) (x,, x 40 ) 0 ) * x = x+ +x40 40.(ii) 0 x N(0, σ 40 ).(iii) z = x 0 N(0, ) σ 40 σ σ σ z σ = i= (x i x) z = x 0 () σ 40 z N(0, ) ˆσ σ () Gosset () t x,, x 40 z z () () t t () * t

3 t t () t t t t σ σ σ t () *3 39 t *4 t N(0, ) (() z t t ) t x,, x N(µ, σ ) t = x µ σ ( x = i= x i, σ = (x i x) ) i= ( ) t t( ) t( ) (00 α) t(, α) () σ t 4 χ 4. x,, x N(0, ) ( ) χ = x + + x (3) * t (3) χ x,, x N(0, ) χ χ χ () (00 α) χ (, α) χ χ = x ( N(0, ) ) = ( χ ) *3 χ χ (i) σ ( ) ( ) *4 σ σ σ * 3

4 N(0, ) χ () N(0, ). χ (). z N(0, ) χ = z *6 χ χ () N(0, ). 97. χ = (z(0.97)) (= 3.84) χ () z = z = z(0.97) =.96, z(0.0) =.96 z = >.96 N(0, ). z = <.96 N(0, ). z χ = 4 χ = (z(0.97)) = 3.84 χ > χ χ = z z(0.0) = z(0.97) χ = (z(0.0)) χ > χ z < z(0.0) z(0.97) < z (4) P r(z < z(0.0) z(0.97) < z) = 0.0 P r (χ > χ ) = 0.0 *7 χ χ () χ χ () χ = χ (, 0.9) (. ) = ( χ ) (z(0.97)) = χ (, 0.9) (z( α)) = χ (, α) (4) χ (z(0.97) =.96) 3.84 χ () (χ (, 0.9) = 3.84) *6 χ z z *7 χ χ 4

5 χ χ *8 x,, x N(0, ) χ x,, x N(0, ) χ = x + x χ χ () χ () 00 α χ (, α) (i)χ χ (), χ χ (m) χ + χ χ ( + m) (ii) x N(µ, σ ), x N(µ, σ ),, x N(µ, σ ) ) χ = (x µ ) σ + + (x µ ) σ χ (ii) x i µ i σ i (iii) ((ii) ) x,, x N(µ, σ )( χ = (x µ) σ + + (x µ) σ χ 4. (iii) 4.. (iii) µ σ µ x, x N(µ, σ ) x = i= σ = x i (x i x) i= ( ) σ σ = σ i= (x i x) = (x x) σ + (x x) σ + + (x x) σ χ ( ) (iii) µ x *9 *8 χ *9

6 4.. A B C A x, x, x 3, x 4, x N(µ, σ ) B C x, x, x 3, x 4, x N(µ, σ ) x 3, x 3, x 33, x 34, x 3 N(µ 3, σ ) ( σ ) µ = µ = µ 3 * 0 :µ = µ = µ 3 χ x = x = x 3 = j= j= j= x j x j x 3j N N N ) (µ, σ ) (µ, σ ) (µ 3, σ x = 3 (x + x + x 3 ) = 3 i= j= x ij ( µ + µ + µ ) 3 N, σ 3 µ = µ = µ 3 µ ( ) x, x, x 3 N µ, σ χ = σ 3 (x i x) i= χ () σ χ (, 0.9) < χ * *0 * χ χ 6

7 F. t A B C A x, x, x 3, x 4, x N(µ, σ ) B C x, x, x 3, x 4, x N(µ, σ ) x 3, x 3, x 33, x 34, x 3 N(µ 3, σ ) ( σ ) µ = µ = µ 3 * ( ) µ = µ = µ 3 µ x, x, x 3 N µ, σ χ = σ 3 (x i x) () i= χ σ t σ A,B,C σ σ A = 4 σ B = 4 σ C = 4 (x j x ) j= (x j x ) j= (x 3j x 3 ) j= χ = (x x) σ A + (x x) σ B + (x 3 x) σ C σ σ ˆ A, σ ˆ B, σ ˆ C σ 4 σ A σ, 4 σ B σ, 4 σ C σ 4 χ χ (i) 4 σ A σ + 4 σ B σ + 4 σ C σ = j= (x j x ) σ + j= (x j x ) σ + (x 3j x 3 ) j= σ (6) * 7

8 χ χ * 3 σ = (4 σ A + 4 σ B + 4 σ C ) = 3 ( σ A + σ B + σ C ) σ A, σ B, σ C σ * 4 () σ σ χ = σ 3 (x i x) i= χ F σ σ σ χ = σ 3 i= (x i x) σ σ χ χ = σ 3 i= (x i x) σ σ * () χ χ χ / F F = σ 3 i= (x i x) σ σ = χ χ F (,) F * 6*7 (,) F 9 F (,, 0.9) * 8 F > F (,, 0.9) χ t χ.. F χ χ (), χ χ (m)( ) F = (, m) F F (, m) * 9 F (, m) (00 α) F (, m, α) χ χ m *3 χ χ E[χ ] = *4 σ (6) σ χ * σ χ σ χ *6 - *7 χ F *8 χ F *9, m m 8

9 .. (),, I ( N = I ) σ µ = = µ I x,, x N(µ, σ ) x,, x N(µ, σ ).. I x I,, x I N(µ I, σ ) x = x j,, x I = j= j= x Ij, x = I ( µ = = µ I µ x,, x I N I i= j= µ, σ x ij ) χ = (x x) σ + + (x I x) σ = σ I (x i x) (7) i= (I ) χ σ σ σ σ = = σ = σ =.. σ I = (x j x ) j= (x j x ) j= (x Ij x I ) j= I( ) (( ) σ + + ( ) σ I ) I( ) I i= j= (x ij x i ) I( ) σ σ = (x x ) σ + + (x I x I ) σ χ (I( )) 9

10 (7) σ σ χ = σ = σ I (x i x) i= = χ σ σ = I i= (x i x) σ σ χ I( ) I( ) σ σ χ (7) (I ) χ σ σ = I( ) I( ) σ σ I( ) χ χ F = I χ = I( ) I( ) σ σ I χ (I, I( )) F * 0 F > F (I, I( ), 0.9). F F χ F = t χ * F χ χ *.. F F σ I σ = (x ij x) i= j= χ.. F I = ( = t F χ (t(m, α)) = F (, m, α) *0 F χ = σ I i= (x i x) I * I i= (x i x) = σ I i= (x i x) i= j= (x ij x i ) * 0

11 6, t, ) χ ) F

(iii) x, x N(µ, ) z = x µ () N(0, ) () 0 (y,, y 0 ) (σ = 6) *3 0 y y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y ( ) *4 H 0 : µ

(iii) x, x N(µ, ) z = x µ () N(0, ) () 0 (y,, y 0 ) (σ = 6) *3 0 y y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y ( ) *4 H 0 : µ t 2 Armitage t t t χ 2 F χ 2 F 2 µ, N(µ, ) f(x µ, ) = ( ) exp (x µ)2 2πσ 2 2 0, N(0, ) (00 α) z(α) t * 2. t (i)x N(µ, ) x µ σ N(0, ) 2 (ii)x,, x N(µ, ) x = x + +x ( N µ, σ2 ) (iii) (i),(ii) x,, x N(µ,

More information

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H 1 1 1.1 *1 1. 1.3.1 n x 11,, x 1n Nµ 1, σ x 1,, x n Nµ, σ H 0 µ 1 = µ = µ H 1 µ 1 µ H 0, H 1 * σ σ 0, σ 1 *1 * H 0 H 0, H 1 H 1 1 H 0 µ, σ 0 H 1 µ 1, µ, σ 1 L 0 µ, σ x L 1 µ 1, µ, σ x x H 0 L 0 µ, σ 0

More information

II (No.2) 2 4,.. (1) (cm) (2) (cm) , (

II (No.2) 2 4,.. (1) (cm) (2) (cm) , ( II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0,

More information

I? 3 1 3 1.1?................................. 3 1.2?............................... 3 1.3!................................... 3 2 4 2.1........................................ 4 2.2.......................................

More information

20 15 14.6 15.3 14.9 15.7 16.0 15.7 13.4 14.5 13.7 14.2 10 10 13 16 19 22 1 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 2,500 59,862 56,384 2,000 42,662 44,211 40,639 37,323 1,500 33,408 34,472

More information

- 2 -

- 2 - - 2 - - 3 - (1) (2) (3) (1) - 4 - ~ - 5 - (2) - 6 - (1) (1) - 7 - - 8 - (i) (ii) (iii) (ii) (iii) (ii) 10 - 9 - (3) - 10 - (3) - 11 - - 12 - (1) - 13 - - 14 - (2) - 15 - - 16 - (3) - 17 - - 18 - (4) -

More information

2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1

2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1 1 1979 6 24 3 4 4 4 4 3 4 4 2 3 4 4 6 0 0 6 2 4 4 4 3 0 0 3 3 3 4 3 2 4 3? 4 3 4 3 4 4 4 4 3 3 4 4 4 4 2 1 1 2 15 4 4 15 0 1 2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4

More information

1 (1) (2)

1 (1) (2) 1 2 (1) (2) (3) 3-78 - 1 (1) (2) - 79 - i) ii) iii) (3) (4) (5) (6) - 80 - (7) (8) (9) (10) 2 (1) (2) (3) (4) i) - 81 - ii) (a) (b) 3 (1) (2) - 82 - - 83 - - 84 - - 85 - - 86 - (1) (2) (3) (4) (5) (6)

More information

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,. (1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..

More information

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,. 24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)

More information

..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A

..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A .. Laplace ). A... i),. ω i i ). {ω,..., ω } Ω,. ii) Ω. Ω. A ) r, A P A) P A) r... ).. Ω {,, 3, 4, 5, 6}. i i 6). A {, 4, 6} P A) P A) 3 6. ).. i, j i, j) ) Ω {i, j) i 6, j 6}., 36. A. A {i, j) i j }.

More information

医系の統計入門第 2 版 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, 第 2 版 1 刷発行時のものです.

医系の統計入門第 2 版 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, 第 2 版 1 刷発行時のものです. 医系の統計入門第 2 版 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/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987

More information

研修コーナー

研修コーナー l l l l l l l l l l l α α β l µ l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

More information

( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1

( )/2   hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1 ( )/2 http://www2.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html 1 2011 ( )/2 2 2011 4 1 2 1.1 1 2 1 2 3 4 5 1.1.1 sample space S S = {H, T } H T T H S = {(H, H), (H, T ), (T, H), (T, T )} (T, H) S

More information

untitled

untitled ( ) 200133 3 3 3 3, 7 347 57 10 i ii iii -1- -2- -3- -4- 90011001700mm -5- 4.2 1991 73.5 44.4 7.4 10.5 10.5 7.4 W 3 H 2.25 H 2.25 7.4 51.8 140.6 88.8 268.8m 5,037.9m 2 2mm 16cm916cm 10.5 W 3 H 2.25 62.8

More information

分散分析・2次元正規分布

分散分析・2次元正規分布 2 II L10(2016-06-30 Thu) : Time-stamp: 2016-06-30 Thu 13:55 JST hig F 2.. http://hig3.net ( ) L10 2 II(2016) 1 / 24 F 2 F L09-Q1 Quiz :F 1 α = 0.05, 2 F 3 H 0, : σ 2 1 /σ2 2 = 1., H 1, σ 2 1 /σ2 2 1. 4

More information

読めば必ずわかる 分散分析の基礎 第2版

読めば必ずわかる 分散分析の基礎 第2版 2 2003 12 5 ( ) ( ) 2 I 3 1 3 2 2? 6 3 11 4? 12 II 14 5 15 6 16 7 17 8 19 9 21 10 22 11 F 25 12 : 1 26 3 I 1 17 11 x 1, x 2,, x n x( ) x = 1 n n i=1 x i 12 (SD ) x 1, x 2,, x n s 2 s 2 = 1 n n (x i x)

More information

統計学のポイント整理

統計学のポイント整理 .. September 17, 2012 1 / 55 n! = n (n 1) (n 2) 1 0! = 1 10! = 10 9 8 1 = 3628800 n k np k np k = n! (n k)! (1) 5 3 5 P 3 = 5! = 5 4 3 = 60 (5 3)! n k n C k nc k = npk k! = n! k!(n k)! (2) 5 3 5C 3 = 5!

More information

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2)

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2) (1) I 44 II 45 III 47 IV 52 44 4 I (1) ( ) 1945 8 9 (10 15 ) ( 17 ) ( 3 1 ) (2) 45 II 1 (3) 511 ( 451 1 ) ( ) 365 1 2 512 1 2 365 1 2 363 2 ( ) 3 ( ) ( 451 2 ( 314 1 ) ( 339 1 4 ) 337 2 3 ) 363 (4) 46

More information

6.1 (P (P (P (P (P (P (, P (, P.

6.1 (P (P (P (P (P (P (, P (, P. (011 30 7 0 ( ( 3 ( 010 1 (P.3 1 1.1 (P.4.................. 1 1. (P.4............... 1 (P.15.1 (P.16................. (P.0............3 (P.18 3.4 (P.3............... 4 3 (P.9 4 3.1 (P.30........... 4 3.

More information

.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T

.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977

More information

i ii i iii iv 1 3 3 10 14 17 17 18 22 23 28 29 31 36 37 39 40 43 48 59 70 75 75 77 90 95 102 107 109 110 118 125 128 130 132 134 48 43 43 51 52 61 61 64 62 124 70 58 3 10 17 29 78 82 85 102 95 109 iii

More information

³ÎΨÏÀ

³ÎΨÏÀ 2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p

More information

SC-85X2取説

SC-85X2取説 I II III IV V VI .................. VII VIII IX X 1-1 1-2 1-3 1-4 ( ) 1-5 1-6 2-1 2-2 3-1 3-2 3-3 8 3-4 3-5 3-6 3-7 ) ) - - 3-8 3-9 4-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 5-10 5-11

More information

<4D6963726F736F667420506F776572506F696E74202D208376838C835B83938365815B835683878393312E707074205B8CDD8AB78382815B83685D>

<4D6963726F736F667420506F776572506F696E74202D208376838C835B83938365815B835683878393312E707074205B8CDD8AB78382815B83685D> i i vi ii iii iv v vi vii viii ix 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

More information

A, B, C. (1) A = A. (2) A = B B = A. (3) A = B, B = C A = C. A = B. (3)., f : A B g : B C. g f : A C, A = C. 7.1, A, B,. A = B, A, A A., A, A

A, B, C. (1) A = A. (2) A = B B = A. (3) A = B, B = C A = C. A = B. (3)., f : A B g : B C. g f : A C, A = C. 7.1, A, B,. A = B, A, A A., A, A 91 7,.,, ( ).,,.,.,. 7.1 A B, A B, A = B. 1), 1,.,. 7.1 A, B, 3. (i) A B. (ii) f : A B. (iii) A B. (i) (ii)., 6.9, (ii) (iii).,,,. 1), Ā = B.. A, Ā, Ā,. 92 7 7.2 A, B, C. (1) A = A. (2) A = B B = A. (3)

More information

幕末期の貨幣供給:万延二分金・銭貨を中心に

幕末期の貨幣供給:万延二分金・銭貨を中心に 1858 67 1 1860 61 2 1862 65 3 1866 67 83 E-mail: noriko.fujii-1@boj.or.jp / /2016.4 67 1. 1859 6 1867 3 1868 4 4 1860 1978, 1980 1987 1988 1863 3 1976 1981 2004 1875 8 1963 1858 5 69 2 2.5 2 68 /2016.4

More information

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 () - 1 - - 2 - - 3 - - 4 - - 5 - 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

More information

6.1 (P (P (P (P (P (P (, P (, P.101

6.1 (P (P (P (P (P (P (, P (, P.101 (008 0 3 7 ( ( ( 00 1 (P.3 1 1.1 (P.3.................. 1 1. (P.4............... 1 (P.15.1 (P.15................. (P.18............3 (P.17......... 3.4 (P................ 4 3 (P.7 4 3.1 ( P.7...........

More information

1,000 700-1 -

1,000 700-1 - 23 9 () - 0 - 1,000 700-1 - 2 3 ( 16:0017:00 ( 8:15 8:30 10:3010:50 8:00 8:10 8:10 9:30 11:0011:20 11:3015:30 16:0016:40 16:0016:10 16:50 21:00 4:00 4:006:00 6:00 6:1511:00 11:3012:00 12:3014:30 (1) ()

More information

untitled

untitled 2 : n =1, 2,, 10000 0.5125 0.51 0.5075 0.505 0.5025 0.5 0.4975 0.495 0 2000 4000 6000 8000 10000 2 weak law of large numbers 1. X 1,X 2,,X n 2. µ = E(X i ),i=1, 2,,n 3. σi 2 = V (X i ) σ 2,i=1, 2,,n ɛ>0

More information

1 10 1113 14 1516 1719 20 21 22 2324 25 2627 i 2829 30 31 32 33 3437 38 3941 42 4344 4547 48 4950 5152 53 5455 ii 56 5758 59 6061 iii 1 2 3 4 5 6 7 8 9 10 PFI 30 20 10 PFI 11 12 13 14 15 10 11 16 (1) 17

More information

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >

More information

18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C

18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C 8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,

More information

,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = , ( ) : = F 1 + F 2 + F 3 + ( ) : = i Fj j=1 2

,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = , ( ) : = F 1 + F 2 + F 3 + ( ) : = i Fj j=1 2 6 2 6.1 2 2, 2 5.2 R 2, 2 (R 2, B, µ)., R 2,,., 1, 2, 3,., 1, 2, 3,,. () : = 1 + 2 + 3 + (6.1.1).,,, 1 ,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = 1 + 2 + 3 +,

More information

これわかWord2010_第1部_100710.indd

これわかWord2010_第1部_100710.indd i 1 1 2 3 6 6 7 8 10 10 11 12 12 12 13 2 15 15 16 17 17 18 19 20 20 21 ii CONTENTS 25 26 26 28 28 29 30 30 31 32 35 35 35 36 37 40 42 44 44 45 46 49 50 50 51 iii 52 52 52 53 55 56 56 57 58 58 60 60 iv

More information

パワポカバー入稿用.indd

パワポカバー入稿用.indd i 1 1 2 2 3 3 4 4 4 5 7 8 8 9 9 10 11 13 14 15 16 17 19 ii CONTENTS 2 21 21 22 25 26 32 37 38 39 39 41 41 43 43 43 44 45 46 47 47 49 52 54 56 56 iii 57 59 62 64 64 66 67 68 71 72 72 73 74 74 77 79 81 84

More information

これでわかるAccess2010

これでわかるAccess2010 i 1 1 1 2 2 2 3 4 4 5 6 7 7 9 10 11 12 13 14 15 17 ii CONTENTS 2 19 19 20 23 24 25 25 26 29 29 31 31 33 35 36 36 39 39 41 44 45 46 48 iii 50 50 52 54 55 57 57 59 61 63 64 66 66 67 70 70 73 74 74 77 77

More information

.. ( )T p T = p p = T () T x T N P (X < x T ) N = ( T ) N (2) ) N ( P (X x T ) N = T (3) T N P T N P 0

.. ( )T p T = p p = T () T x T N P (X < x T ) N = ( T ) N (2) ) N ( P (X x T ) N = T (3) T N P T N P 0 20 5 8..................................................2.....................................3 L.....................................4................................. 2 2. 3 2. (N ).........................................

More information

FX ) 2

FX ) 2 (FX) 1 1 2009 12 12 13 2009 1 FX ) 2 1 (FX) 2 1 2 1 2 3 2010 8 FX 1998 1 FX FX 4 1 1 (FX) () () 1998 4 1 100 120 1 100 120 120 100 20 FX 100 100 100 1 100 100 100 1 100 1 100 100 1 100 101 101 100 100

More information

(個別のテーマ) 薬剤に関連した医療事故

(個別のテーマ) 薬剤に関連した医療事故 - 67 - III - 68 - - 69 - III - 70 - - 71 - III - 72 - - 73 - III - 74 - - 75 - III - 76 - - 77 - III - 78 - - 79 - III - 80 - - 81 - III - 82 - - 83 - III - 84 - - 85 - - 86 - III - 87 - III - 88 - - 89

More information

(個別のテーマ) 放射線検査に関連した医療事故

(個別のテーマ) 放射線検査に関連した医療事故 - 131 - III - 132 - - 133 - III - 134 - - 135 - III - 136 - - 137 - III - 138 - - 139 - III - 140 - - 141 - III - 142 - - 143 - III - 144 - - 145 - III - 146 - - 147 - III - 148 - - 149 - III - 150 - -

More information

平成18年版 男女共同参画白書

平成18年版 男女共同参画白書 i ii iii iv v vi vii viii ix 3 4 5 6 7 8 9 Column 10 11 12 13 14 15 Column 16 17 18 19 20 21 22 23 24 25 26 Column 27 28 29 30 Column 31 32 33 34 35 36 Column 37 Column 38 39 40 Column 41 42 43 44 45

More information

st.dvi

st.dvi 9 3 5................................... 5............................. 5....................................... 5.................................. 7.........................................................................

More information

EV200R I II III 1 2 3 4 5 6 7 8 9 10 1 2 3 11 4 5 12 6 13 1 2 14 3 4 15 5 16 1 2 17 3 18 4 5 19 6 20 21 22 123 456 123 456 23 1 2 24 3 4 25 5 3 26 4 5 6 27 7 8 9 28 29 30 31 32 1 2 33 3 4 34 1 35 2 1

More information

訪問看護ステーションにおける安全性及び安定的なサービス提供の確保に関する調査研究事業報告書

訪問看護ステーションにおける安全性及び安定的なサービス提供の確保に関する調査研究事業報告書 1... 1 2... 3 I... 3 II... 3 1.... 3 2....15 3....17 4....19 5....25 6....34 7....38 8....48 9....58 III...70 3...73 I...73 1....73 2....82 II...98 4...99 1....99 2....104 3....106 4....108 5.... 110 6....

More information

SFGÇÃÉXÉyÉNÉgÉãå`.pdf

SFGÇÃÉXÉyÉNÉgÉãå`.pdf SFG 1 SFG SFG I SFG (ω) χ SFG (ω). SFG χ χ SFG (ω) = χ NR e iϕ +. ω ω + iγ SFG φ = ±π/, χ φ = ±π 3 χ SFG χ SFG = χ NR + χ (ω ω ) + Γ + χ NR χ (ω ω ) (ω ω ) + Γ cosϕ χ NR χ Γ (ω ω ) + Γ sinϕ. 3 (θ) 180

More information

1 2 3 4 5 6 X Y ABC A ABC B 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 13 18 30 P331 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 ( ) 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

More information

26 2 3 4 5 8 9 6 7 2 3 4 5 2 6 7 3 8 9 3 0 4 2 4 3 4 4 5 6 5 7 6 2 2 A B C ABC 8 9 6 3 3 4 4 20 2 6 2 2 3 3 4 4 5 5 22 6 6 7 7 23 6 2 2 3 3 4 4 24 2 2 3 3 4 4 25 6 2 2 3 3 4 4 26 2 2 3 3 27 6 4 4 5 5

More information

mogiJugyo_slide_full.dvi

mogiJugyo_slide_full.dvi a 2 + b 2 = c 2 (a, b, c) a 2 a 2 = a a a 1/ 78 2/ 78 3/ 78 4/ 78 180 5/ 78 http://www.kaijo.ed.jp/ 6/ 78 a, b, c ABC C a b B c A C 90 a 2 + b 2 = c 2 7/ 78 C a b a 2 +b 2 = c 2 B c A a 2 a a 2 = a a 8/

More information

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t 6 6.1 6.1 (1 Z ( X = e Z, Y = Im Z ( Z = X + iy, i = 1 (2 Z E[ e Z ] < E[ Im Z ] < Z E[Z] = E[e Z] + ie[im Z] 6.2 Z E[Z] E[ Z ] : E[ Z ] < e Z Z, Im Z Z E[Z] α = E[Z], Z = Z Z 1 {Z } E[Z] = α = α [ α ]

More information

ad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign(

ad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign( I n n A AX = I, YA = I () n XY A () X = IX = (YA)X = Y(AX) = YI = Y X Y () XY A A AB AB BA (AB)(B A ) = A(BB )A = AA = I (BA)(A B ) = B(AA )B = BB = I (AB) = B A (BA) = A B A B A = B = 5 5 A B AB BA A

More information

ii 3.,. 4. F. (), ,,. 8.,. 1. (75% ) (25% ) =9 7, =9 8 (. ). 1.,, (). 3.,. 1. ( ).,.,.,.,.,. ( ) (1 2 )., ( ), 0. 2., 1., 0,.

ii 3.,. 4. F. (), ,,. 8.,. 1. (75% ) (25% ) =9 7, =9 8 (. ). 1.,, (). 3.,. 1. ( ).,.,.,.,.,. ( ) (1 2 )., ( ), 0. 2., 1., 0,. 23(2011) (1 C104) 5 11 (2 C206) 5 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 ( ). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5.. 6.. 7.,,. 8.,. 1. (75%

More information

SO(3) 49 u = Ru (6.9), i u iv i = i u iv i (C ) π π : G Hom(V, V ) : g D(g). π : R 3 V : i 1. : u u = u 1 u 2 u 3 (6.10) 6.2 i R α (1) = 0 cos α

SO(3) 49 u = Ru (6.9), i u iv i = i u iv i (C ) π π : G Hom(V, V ) : g D(g). π : R 3 V : i 1. : u u = u 1 u 2 u 3 (6.10) 6.2 i R α (1) = 0 cos α SO(3) 48 6 SO(3) t 6.1 u, v u = u 1 1 + u 2 2 + u 3 3 = u 1 e 1 + u 2 e 2 + u 3 e 3, v = v 1 1 + v 2 2 + v 3 3 = v 1 e 1 + v 2 e 2 + v 3 e 3 (6.1) i (e i ) e i e j = i j = δ ij (6.2) ( u, v ) = u v = ij

More information

エクセルカバー入稿用.indd

エクセルカバー入稿用.indd i 1 1 2 3 5 5 6 7 7 8 9 9 10 11 11 11 12 2 13 13 14 15 15 16 17 17 ii CONTENTS 18 18 21 22 22 24 25 26 27 27 28 29 30 31 32 36 37 40 40 42 43 44 44 46 47 48 iii 48 50 51 52 54 55 59 61 62 64 65 66 67 68

More information

i

i 14 i ii iii iv v vi 14 13 86 13 12 28 14 16 14 15 31 (1) 13 12 28 20 (2) (3) 2 (4) (5) 14 14 50 48 3 11 11 22 14 15 10 14 20 21 20 (1) 14 (2) 14 4 (3) (4) (5) 12 12 (6) 14 15 5 6 7 8 9 10 7

More information

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ( ) 24 25 26 27 28 29 30 ( ) ( ) ( ) 31 32 ( ) ( ) 33 34 35 36 37 38 39 40 41 42 43 44 ) i ii i ii 45 46 47 2 48 49 50 51 52 53 54 55 56 57 58

More information

untitled

untitled i ii (1) (1) (2) (1) (3) (1) (1) (2) (1) (3) (1) (1) (2) (1) (3) (2) (3) (1) (2) (3) (1) (1) (1) (1) (2) (1) (3) (1) (2) (1) (3) (1) (1) (1) (2) (1) (3) (1) (1) (2) (1) (3)

More information