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
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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
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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,
* 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
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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
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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
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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
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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/
(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
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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 ]
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I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )
I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17
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
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
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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
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