0 (1 ) 0 (1 ) 01 Excel Excel ( ) = Excel Excel = =5-5 3 =5* 5 10 =5/ 5 5 =5^ 5 5 ( ), 0, Excel, Excel 13E E

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "0 (1 ) 0 (1 ) 01 Excel Excel ( ) = Excel Excel =5+ 5 + 7 =5-5 3 =5* 5 10 =5/ 5 5 =5^ 5 5 ( ), 0, Excel, Excel 13E+05 13 10 5 13000 13E-05 13 10 5 0000"

Transcription

1 1 ( S/E) (1 ) 01 Excel (-4 ) (5-7 ) Simplex 1 4 (shadow price) 14 5 (reduced cost) 14 3 (8-10 ) Excel 3 4 (11-13 )

2 0 (1 ) 0 (1 ) 01 Excel Excel ( ) = Excel Excel = =5-5 3 =5* 5 10 =5/ 5 5 =5^ 5 5 ( ), 0, Excel, Excel 13E E E E ( ),, 13E , (F) ( ),, ( ) ( ) $, =A1 =$A$1 ( ) ( ) =A$1 =$A1, F4, ( ),, (-4 ), (5-7 ), Excel,, (V), (I),

3 r, ( + ) 1% r = 001 x (x ) y, y 1 1 x = 10000, r = 01 (10%) 0 10,000 1,000 11, ,000 1,100 1,100 1,100 1,10 13, ,310 1,331 14, ,641 1,464 16, ,105 1,611 17, ,716 1,77 19, ,487 1,949 1, ,436,144 3, ,487, x = 10000, r = 01, y = 7 r, y, 1 70 bababababababababababababababab y r = 70 (r ) x, x r, 1 x(1 + r) + = x + xr = x (1 + r) 1 + r, 1 x (1 + r),, y x (1 + r) y y (= x), x (1 + r) y = x x, x (1 + r) y = y, y log(1 + r) = log

4 4 0 (1 ) log(1 + r),, log(1 + r) = r r log = 0693, yr = 0693 r ( ) 05 35%, ( ) r, 70 y r = 70 bababababababababababababababab 7 y r = 7 (r ) 6 9%, ( ) r, 7 y r = 7 7,, %, 01%, 0 3% 100 1, 1 1, 1 1, 1

5 5 1 (-4 ) , , , ( ), p = 1 0 a p, a,,, ( ) = ( ) = ( ) a, p,, p = 0 1 a ( ) = ( = (

6 6 bababababababababababababababab 1 (-4 ) = =,, ( ), p p = a X 1 0 X a 75, 75, 75 (6677) (75 (75 ) = ) 6677 (75 = ) 6677 bababababababababababababababab X = X X = X X 0 1, ,300 80, ,900 (006 13,860 ) 65, 794, %, % ( ) 65, 50% 1%

7 ( ) 100,000, 0% 100,000 1,000,000, 18% 1,000,000, 15%, 100 ( 15%) , 0% 1 31, 0% 15% = 5% (5 ), ( 15%) , 15% 1 31 (30 ) , , 170, 00 15%, 5 5, ( ) 1, 1 1 ( ) %,

8 8 1 (-4 ) 11 ( ) (0 ) 1 ( 1) 0 0, 1, % ( ) 01% 60 81, 40 ( 40 ) :, 13 ( ) 0, %, % = , 35 3%, 1,, = %, 1,, , 1 35, , 35 = 0

9 9 (5-7 ) x 4y + 6z = 1 (1) 3x + y + z = 11 () x 3y 3z = 14 (3), (1) x y + 3z = 6 (4) () (4) 3, () x, (3) (4), (3) x 7y 7z = 7 (5) y 6z = 0 (6) (5) 7 y z = 1 (7) (6) (7), (6) y, 7z = 1 (9) z = 3 (10) z z (7) y, (4) x y = (1) x = 1 (11)

10 10 (5-7 ) (1) x 4y + 6z = () 3x + y + z = (3) x 3y 3z = (4) (1) x y + 3z = (5) () (4) 3 7y 7z = (6) (3) (4) y 6z = (7) (5) 7 y z = (8) (4) + (7) x + z = (9) (6) + (7) 7z = (10) (9) ( 7) z = (11) (8) (10) x = (1) (7) + (10) y = , (1) x 4y + 6z = () 3x + y + z = (3) x 3y 3z = (4) (1) (5) () (4) (6) (3) (4) (8) (4) + (7) (7) (5) (9) (6) + (7) (11) (8) (10) x = (1) (7) + (10) y = (10) (9) ( 7) z = x 3y + 6z = 15 x + 4y + z = 10 x + y + 6z = 1

11 11 A B, X Y 1 X, A B, 1 Y, 6 A 1 B X Y A 60, B 0, X Y X x, Y y, A x + 6y A 60, x + 6y 60 B, x + y 0 x, y, x 0, y 0,,, p p = 9x + 16y y 0 y = x (6, 8) y = 1 3 x x,,, p (6, 8) p max p = = 18 18, X 6, Y 8

12 1 bababababababababababababababab (5-7 ) = A, B x + 6y = = 60 x + y = = 0, 3 Simplex,, ( ) Smplex X x, Y y, x + 6y 60 x + y 0, ( ) a 0, b 0, a, b, A, B x + 6y + a = 60 x + y + b = 0 (A) (B) p = 9x + 16y 9x 16y + p = 0 (P ) Simplex, 3 (A), (B), (P ) 1 ( ) x y a b p (A) (B) (P ) 1/3 1 1/ /3 0 1/ /3 0 8/ /5 1/5 0 8 (Y ) y a 1 5 b = /10 3/5 0 6 (X) x 1 10 a b = /10 11/ ( ) 3 10 a b + p = 18 Simplex, 3 10 a + 11 b + p = 18 ( ) 5

13 3 Simplex 13 p (a 0, b 0), a, b, p a = b = 0, p (X), (Y ), max p = 18 y a 1 5 b = 8 (Y ) x 1 10 a b = 6 (X) a = b = 0, X, Y x = 6, y = 8 a = b = 0,, ( ) ),, x y a b p (10) (0) /3 1 1/ (30) 5/3 0 1/ (6) 11/3 0 8/ /5 1/ /10 3/ /10 11/ ) ( 9, 16),, ( ) ), 3) ( 1 ), 1), ( 1 ) 4), 1), p

14 14 (5-7 ) 4 (shadow price) x, y, a, b p x + 6y + a = 60 x + y + b = 0 (A) (B) 9x 16y + p = 0 (P ) 3 10 a + 11 b + p = 18 ( ) 5 (x = 0, y = 0), (A), (B), a A, b B (P ) p = 0 a = 60, b = 0, p = 0 ( ), = , 11 5 bababababababababababababababab 3 10, 11 5,,, (shadow price) = (reduced cost) 3, X, Y 6, 0, X, Y p = 6x + 0y, (0, 10) p y 0 y = x + 0 (0, 10) y = 1 3 x x (x, y) = (0, 10) p max p = = = 60, = 10, B 10

15 5 (reduced cost) 15 Simplex 1 x y a b p (10) (0) /3 1 1/ /3 0 1/ /3 0 10/ , 3 x + 10 a + p = 00 ( ) 3 p, x a, x = 0, a = 0, p x = 0, a = 0, max p = 00, 1 3 x + y a = 10, 5 3 x 1 6 a + b = 10 x 0, a 0 x = 0, a = 0, y, b y = 10, b = 10, x = 0, y = 10 ( ), max p = 00 ( ), A, B 10 ( ) ( ), 10 3 (shadow price), = 00 3 (reduced cost) X 1, 3, X 1, 3 ( )

16 16 (5-7 ) 1 X Y, A, 1, B 1, A B 10, 150 X, Y, 3, Simplex X, Y, Z, A 1, B, 3, 0 C 1,, 1 A, B, C 10, 4, 16 X, Y, Z 3, 5,, X, Y, Z,, L 3 ( ) X Y, x, y Y 4 Z z, z = 3y Y C x, C y ( : ) C x = x x, C y = 03y 4z X, Y, 1 1, 101 x + y , C = C x + C y ( : x = 360, y = 650, C = 1435) p = 61, R ( : x = 35, y = 635, R = 13949)

17 17 3 (8-10 ) 31, 1 ( Excel ) (AVERAGE) x 1, x, x 3,, x,, x (VARP ) x = x 1 + x + + x x i x x i x,, V (x), (kg ) V (x) = (x 1 x) + (x x) + + (x x) (STDEVP ) V (x) σ(x) (kg) σ(x) = V (x) (MAX) (MI) (MAX()-MI() ) (MODE) (MEDIA), ( + 1)/, / ( +)/, V (x) = x ( x) bababababababababababababababab (x ) = (x ) (x ) x = xi

18 18 3 (8-10 ), (xi x) V (x) = (x = i x x i + x ) x = i x xi + x x = i x x + x = x x x i (i = 1,,, ), x, σ(x) x bababababababababababababababab z z, x ( ) z i = x i x σ(x) (x ), (11-14 ), 0, 1 z = 0, σ(z) = 1, x i t i t i = z i t i = x i x σ(x) 50, 10 t = 50, σ(t) = 10 3 ( ) x, y, x, y (covariance) Cov(x, y) = 1 (x i x)(y i ȳ) i=1 = (x 1 x)(y 1 ȳ) + (x x)(y ȳ) + + (x x)(y ȳ) x x Cov(x, y),, x Cov(x, x) = V (x) Cov(x, y) = xy x ȳ (x,y ) = (x y ) (x ) (y )

19 33 19 x, y ( Peason ) r Cov(x, y) r = σ(x) σ(y) (xi x)(y i ȳ) = (xi x) (yi ȳ) x i, y i, x y y i Cauchy-Schwarz pq p q, r bababababababababababababababab 1 1 (r) 1 33 x i, y i, x i y i,, x i y i, ŷ i, ŷ i = a + bx i, ŷ, a, b a, b,, E E = a 8ab + 11b + 4a 14b + 9 = (a 4ab + a) + 11b 14b + 9 = (a (b 1)) (b 1) + 11b 14b + 9 = (a b + 1) + 3b 6b + 7 = (a b + 1) + 3(b 1) + 4 0, E 4 min E = 4 E a b + 1 = 0, b 1 = 0, a = b = 1

20 0 3 (8-10 ) (1) ŷ i y i e i e i e i = y i ŷ i y = a + bx, E, a, b E = (y i ŷ i ) i=1 = (y i a bx i ) = a + ab x i + b x i a y i b x i y i + yi ( = a + b ) x i yi ( x + i ( xi ) ) xi y i b xi yi x i ( xi ) + Const = (a + bx y) + V (x) ( b ) Cov(x, y) + Const V (x) Const, a + b x ȳ = 0, b Cov(x, y) V (x), E Const bababababababababababababababab, = 0 ŷ = a + bx, b = Cov(x, y), a = ȳ b x V (x)

21 33 1 () E, E a E = (y i a bx i ) E a = (y i a bx i ) E, 0,, yi a b xi = 0 a = ȳ b x ( ) E b E b = x i (y i a bx i ) E 0, xi y i 0 = a xi x b i xi y i x = (ȳ b x) x b i ( ) ( ) xi y i x = x ȳ b i x = Cov(x, y) b V (x) a b a = ȳ b x, b = Cov(x, y) V (x) bababababababababababababababab ŷ, ŷ = y, ŷ y, ŷ = a + bx = a + b x = ȳ

22 3 (8-10 ) 34 ŷ i V (ŷ), y i V (y) R R = V (ŷ) V (y), bababababababababababababababab R 1 0 (R ) 1, y, 1, x ( R ) = 1 (ŷ ŷ) V (y) (a + bxi a b x) = 1 V (y) = 1 V (y) b (xi x) = 1 Cov(x, y) V (y) V (x) V (x) = Cov(x, y) V (x)v (y) = ( r), 35 3 x i, y i, z i, z i x i y i 1, z i ẑ i, ẑ i = a + bx i + cy i a b, c E,, E = (z i ẑ) a, = (z i a bx i cy i ) E a = (z i a bx i cy i ) = ( z a b x cȳ)

23 36 Excel 3 b, c, E b = x i (z i a bx i cy i ) ( ) = xz a x bx cxy E c = y i (z i a bx i cy i ) ) = (yz aȳ bxy cy E, 0, a, b, c 3 z a b x cȳ = 0 xz a x bx cxy = 0 yz aȳ byx cy = 0 z, xz, yz, z 1 x y a xz = x x xy b yz y yx y, a b, c a 1 x y b = x x xy c y yx y 1 c z xz yz y, m x j (j = 1,,, m), ŷ = a 0 + a 1 x 1 + a x + + a m x m, a j (j = 0, 1,,, m), a 0 1 x 1 x m a 1 = x 1 x 1 x 1 x m a m x m x m x 1 x m 1 ȳ x 1 y x m y 36 Excel Excel MMULT(), MIVERSE() Ctrl Shift, Enter

24 4 3 (8-10 ) 31 5 ( ),, z = (x x)/σ(x), t = 10z ( ) X Y 5 Y X, b = Cov(x, y)/v (x), a = ȳ b x 33 ( ) 15 X, Y, Z Z X Y, Excel MIVERSE(), MMULT()

25 5 4 (11-13 ) , / (x k ) (f k ) (f k /) () 1 f k ( = 100 ) n ( n = 7 ), x, V (x), σ(x) x = x 1f 1 + x f + + x n f n V (x) = (x 1 x) f 1 + (x x) f + + (x n x) f n = x 1 f 1 + x f + + x n f n σ(x) = V (x) x 41 7, 44 1 V (x) = x ( x) r k = f k /, x = x 1 r 1 + x r + + x n r n V (x) = (x 1 x) r 1 + (x x) r + + (x n x) r n = ( x 1 r 1 + x r + + x n r n ) x, x = = 4994 V (x) = = x k p k, x 1 x x n p 1 p p n 1, ,

26 6 bababababababababababababababab 4 (11-13 ) x = x 1 p 1 + x p + + x n p n V (x) = (x 1 x) p 1 + (x x) p + + (x n x) p n = ( ) x 1 p 1 + x p + + x n p n x σ(x) = V (x) 4 n k nc k, n(n 1)(n ) (n k + 1) nc k = k(k 1)(k ) 1 n! = k! (n k)! k! k, k! = k(k 1) 1 0! = 1, A (A ) P (A), p, A Ā (A ) q A P (A) = p P (Ā) = q (= 1 p) n A k n, k, n k, nc k p k q n k n, p B(n, p) x k : 0 1 k n p k : nc 0 q n nc 1 p q n 1 nc k p k q n k nc n p n 1 (p + q) n = n C 0 q n + n C 1 p q n 1 + n C p q n + + n C n p n, p + q = 1, nc 0 q n + n C 1 p q n n C k p k q n k + + n C n p n = 1 p k (k = 0, 1,, n) 1

27 4 7 x, x = = = V (x), V (x) = n x k p k k=0 n k n C k p k q n k k=0 n n! k k! (n k)! pk q n k k=1 n 1 n! = (k + 1) (k + 1)! (n k 1)! pk+1 q n k 1 k=0 = np = np = n 1 k=0 (n 1)! k! (n k 1)! pk q n k 1 n x k p k x k=0 n k=0 k n! k! (n k)! pk q n k (np) n 1 = np (k + 1) = np k=0 n 1 k=1 k = np (n 1)p (n 1)! k! (n k 1)! pk q n k 1 n p (n 1)! k! (n k 1)! pk q n k 1 + np n p n k=0 = n(n 1)p np n p = np(1 p) (n )! k! (n k )! pk q n k np n p bababababababababababababababab B(n, p),, x = np, V (x) = np(1 p), σ(x) = np(1 p)

28 8 4 (11-13 ) COMBI() nc s, n s, nc s = n! s! (n s)! Excel COMBI nc s = COMBI(n, s) BIOMDIST() n, p, s nc s p s (1 p) n s Excel BIOMDIST nc s p s (1 p) n s = BIOMDIST(s, n, p, FALSE), s, 41 s nc k p k (1 p) n k = BIOMDIST(s, n, p, TRUE) k=0, 1 4 p = , C (1 09) 5 = = , P, P = 100 C C C C C C = =

29 m, m, σ (m, σ ) σ, f(x), f(x) = 1 e (x m) /σ πσ X a b, P (a X b) = 1 b e (x m) /σ dx πσ a,, 0, 1 (0, 1) 0, 1, 0 x, x X 1, X,, X n, m, σ X i nm, nσ X X = X 1 + X + + X n nm nσ X,

30 30 4 (11-13 ) 41 ( ) X 1, X,, X n, m, σ ( ) lim P X1 + X + + X n nm x = 1 x e u / du n nσ π, (0, 1) p n B(n, p),, n 4, 1 4 p = , , n = 100, p = 09, np, np(1 p) np = = 90 np(1 p) = (1 09) = 9 90, 3, x = 95, = 167, ( ) 05, 95, = , 0 1, a x < b a x < b,, U(a, b) b x = x 1 a b a dx = 1 b a = a + b [ x ] b a

31 46 31, RAD() b ( V (x) = x 1 a + b a b a dx = 1 [ ] x 3 b ( a + b b a 3 = (b a) 1 a ) Excel RAD() RAD() 0 1, F9, ), (,, ) , , , 50, ( ) 7 95% ( 5%) 1% (%)

32 3 4 (11-13 ) 41 4 p = , , , ,

33 33 5 ( ) S : 1?3? (??)?4? (?15:00??16:00?) E : 1?4? (??)?4? (?15:00??16:00?)

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 1 21 10 5 1 E-mail: qliu@res.otaru-uc.ac.jp 1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 B 1.1.3 boy W ID 1 2 3 DI DII DIII OL OL 1.1.4 2 1.1.5 1.1.6 1.1.7 1.1.8 1.2 1.2.1 1. 2. 3 1.2.2

More information

7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6

7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6 26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7

More information

Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3. 39. 4.. 4.. 43. 46.. 46..

Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3. 39. 4.. 4.. 43. 46.. 46.. Cotets 6 6 : 6 6 6 6 6 6 7 7 7 Part. 8. 8.. 8.. 9..... 3. 3 3.. 3 3.. 7 3.3. 8 Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3.

More information

June 2016 i (statistics) F Excel Numbers, OpenOffice/LibreOffice Calc ii *1 VAR STDEV 1 SPSS SAS R *2 R R R R *1 Excel, Numbers, Microsoft Office, Apple iwork, *2 R GNU GNU R iii URL http://ruby.kyoto-wu.ac.jp/statistics/training/

More information

2 2 MATHEMATICS.PDF 200-2-0 3 2 (p n ), ( ) 7 3 4 6 5 20 6 GL 2 (Z) SL 2 (Z) 27 7 29 8 SL 2 (Z) 35 9 2 40 0 2 46 48 2 2 5 3 2 2 58 4 2 6 5 2 65 6 2 67 7 2 69 2 , a 0 + a + a 2 +... b b 2 b 3 () + b n a

More information

Microsoft Word - 触ってみよう、Maximaに2.doc

Microsoft Word - 触ってみよう、Maximaに2.doc i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x

More information

4 4. A p X A 1 X X A 1 A 4.3 X p X p X S(X) = E ((X p) ) X = X E(X) = E(X) p p 4.3p < p < 1 X X p f(i) = P (X = i) = p(1 p) i 1, i = 1,,... 1 + r + r

4 4. A p X A 1 X X A 1 A 4.3 X p X p X S(X) = E ((X p) ) X = X E(X) = E(X) p p 4.3p < p < 1 X X p f(i) = P (X = i) = p(1 p) i 1, i = 1,,... 1 + r + r 4 1 4 4.1 X P (X = 1) =.4, P (X = ) =.3, P (X = 1) =., P (X = ) =.1 E(X) = 1.4 +.3 + 1. +.1 = 4. X Y = X P (X = ) = P (X = 1) = P (X = ) = P (X = 1) = P (X = ) =. Y P (Y = ) = P (X = ) =., P (Y = 1) =

More information

1 1 3 1.1 (Frequecy Tabulatios)................................ 3 1........................................ 8 1.3.....................................

1 1 3 1.1 (Frequecy Tabulatios)................................ 3 1........................................ 8 1.3..................................... 1 1 3 1.1 (Frequecy Tabulatios)................................ 3 1........................................ 8 1.3........................................... 1 17.1................................................

More information

橡Taro13-EXCEL統計学.PDF

橡Taro13-EXCEL統計学.PDF Excel 4.1 4.1.1 1 X n X,X, 1,Xn X=X X X /n 1 n Excel AVERAGE =AVERAGE Excel MEDIAN 3 =MEDIAN Excel MODE =MODE 4.1. 1 Excel MAX MIN =MAX MIN n X,X,,X X 4-1 1 n V X1-X + X-X + + Xn-X V= n 0 0 Excel VARP

More information

【補足資料】確率・統計の基礎知識

【補足資料】確率・統計の基礎知識 補 足 資 料 確 率 統 計 の 基 礎 知 識 2011 年 3 月 日 本 銀 行 金 融 機 構 局 金 融 高 度 化 センター 1 目 次 1. 基 本 統 計 量 (1 変 量 ) - 平 均 分 散 標 準 偏 差 パーセント 点 2. 基 本 統 計 量 (2 変 量 ) - 散 布 図 共 分 散 相 関 係 数 相 関 行 列 3. 確 率 変 数 - 確 率 変 数 確 率

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

1 1 1 1 1 1 2 f z 2 C 1, C 2 f 2 C 1, C 2 f(c 2 ) C 2 f(c 1 ) z C 1 f f(z) xy uv ( u v ) = ( a b c d ) ( x y ) + ( p q ) (p + b, q + d) 1 (p + a, q + c) 1 (p, q) 1 1 (b, d) (a, c) 2 3 2 3 a = d, c = b

More information

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C 0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,

More information

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y No1 1 (1) 2 f(x) =1+x + x 2 + + x n, g(x) = 1 (n +1)xn + nx n+1 (1 x) 2 x 6= 1 f 0 (x) =g(x) y = f(x)g(x) y 0 = f 0 (x)g(x)+f(x)g 0 (x) 3 (1) y = x2 x +1 x (2) y = 1 g(x) y0 = g0 (x) {g(x)} 2 (2) y = µ

More information

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9 1-1. 1, 2, 3, 4, 5, 6, 7,, 100,, 1000, n, m m m n n 0 n, m m n 1-2. 0 m n m n 0 2 = 1.41421356 π = 3.141516 1-3. 1 0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c),

More information

情報科学概論 第1回資料

情報科学概論 第1回資料 1. Excel (C) Hiroshi Pen Fujimori 1 2. (Excel) 2.1 Excel : 2.2Excel Excel (C) Hiroshi Pen Fujimori 2 256 (IV) :C (C 65536 B4 :2 (2 A3 Excel (C) Hiroshi Pen Fujimori 3 Tips: (1) B3 (2) (*1) (3) (4)Word

More information

2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26 $ $E26 E$26 E$26 $G34 $ E26 F4

2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26 $ $E26 E$26 E$26 $G34 $ E26 F4 1234567 0.1234567 = 2 3 =2+3 =2-3 =2*3 =2/3 =2^3 1:^, 2:*/, 3:+- () =2+3*4 =(2+3)*4 =3*2^2 =(3*2)^2 =(3+6)^0.5 A12 =A12+B12 ( ) ( )0.4 ( 100)0.9 % 1 2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26

More information

ohp.mgp

ohp.mgp 2012/10/09 A/B -- Excel -- !! B video Note-PC Network skype Login Windows Update Web CST Portal Excel Excel ( / ( / /? ( ( [ / /etc..], = ( Excel : (Excel : ( $ [ 1] Excel [ 2] [ 3] Lookup [ 1] [ 2] Excel..

More information

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1. 1.1 1. 1.3.1..3.4 3.1 3. 3.3 4.1 4. 4.3 5.1 5. 5.3 6.1 6. 6.3 7.1 7. 7.3 1 1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N

More information

untitled

untitled 1 1 Excel3 2008.8.19 2 3 10 1 () 4 40596079 2 OK 1 5 341 1 1 6 3-1 A134A135 B135 COUNTIF OK 3-1 7 3 B6B132 1 B135 COUNTIF) OK B6B132 8 2 3-1 3 3-1 3 1 2A133 A134 A135 3B133 SUBTOTAL 9 2 B5B131 OK 4SUBTOTAL

More information

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α 2 2.1. : : 2 : ( ): : ( ): : : : ( ) ( ) ( ) : ( pp.53 6 2.3 2.4 ) : 2.2. ( ). i X i (i = 1, 2,..., n) X 1, X 2,..., X n X i (X 1, X 2,..., X n ) ( ) n (x 1, x 2,..., x n ) (X 1, X 2,..., X n ) : X 1,

More information

II 2014 2 (1) log(1 + r/100) n = log 2 n log(1 + r/100) = log 2 n = log 2 log(1 + r/100) (2) y = f(x) = log(1 + x) x = 0 1 f (x) = 1/(1 + x) f (0) = 1

II 2014 2 (1) log(1 + r/100) n = log 2 n log(1 + r/100) = log 2 n = log 2 log(1 + r/100) (2) y = f(x) = log(1 + x) x = 0 1 f (x) = 1/(1 + x) f (0) = 1 II 2014 1 1 I 1.1 72 r 2 72 8 72/8 = 9 9 2 a 0 1 a 1 a 1 = a 0 (1+r/100) 2 a 2 a 2 = a 1 (1 + r/100) = a 0 (1 + r/100) 2 n a n = a 0 (1 + r/100) n a n a 0 2 n a 0 (1 + r/100) n = 2a 0 (1 + r/100) n = 2

More information

<4D6963726F736F667420576F7264202D204850835483938376838B8379815B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D6963726F736F667420576F7264202D204850835483938376838B8379815B83578B6594BB2D834A836F815B82D082C88C60202E646F63> 例 題 で 学 ぶ Excel 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/084302 このサンプルページの 内 容 は, 第 2 版 発 行 当 時 のものです. i 2 9 2 Web 2 Excel Excel Excel 11 Excel

More information

a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p

a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p a a a a y y ax q y ax q q y ax y ax a a a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p y a xp q y a x p q p p x p p q p q y a x xy xy a a a y a x

More information

(Nov/2009) 2 / = (,,, ) 1 4 3 3 2/8

(Nov/2009) 2 / = (,,, ) 1 4 3 3 2/8 (Nov/2009) 1 sun open-office calc 2 1 2 3 3 1 3 1 2 3 1 2 3 1/8 (Nov/2009) 2 / = (,,, ) 1 4 3 3 2/8 (Nov/2009) 1 (true) false 1 2 2 A1:A10 A 1 2 150 3 200 4 250 5 320 6 330 7 360 8 380 9 420 10 480 (1)

More information

untitled

untitled 11 10 267 6 129 48.3 6 63 2 1 2JIS ME JIS T 1005JIS 1994 1 11 A 10 1999 5 3 13 ME 4 2 11 B B 1999 4 10 267 6 B 7 9 6 10 12 3 11 Excel MODE Excel STANDARDIZE STANDARDIZE(X,)X AVERAGE STDEVP Excel VAR 0.5

More information

aisatu.pdf

aisatu.pdf 1 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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

More information

untitled

untitled 20 7 1 22 7 1 1 2 3 7 8 9 10 11 13 14 15 17 18 19 21 22 - 1 - - 2 - - 3 - - 4 - 50 200 50 200-5 - 50 200 50 200 50 200 - 6 - - 7 - () - 8 - (XY) - 9 - 112-10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 -

More information

untitled

untitled 19 1 19 19 3 8 1 19 1 61 2 479 1965 64 1237 148 1272 58 183 X 1 X 2 12 2 15 A B 5 18 B 29 X 1 12 10 31 A 1 58 Y B 14 1 25 3 31 1 5 5 15 Y B 1 232 Y B 1 4235 14 11 8 5350 2409 X 1 15 10 10 B Y Y 2 X 1 X

More information

xyr x y r x y r u u

xyr x y r x y r u u xyr x y r x y r u u y a b u a b a b c d e f g u a b c d e g u u e e f yx a b a b a b c a b c a b a b c a b a b c a b c a b c a u xy a b u a b c d a b c d u ar ar a xy u a b c a b c a b p a b a b c a

More information

BSE Excel

BSE Excel 200 2 200311110 BSE Excel 1 3 11 1 21 2 20 1 26 2203 2 10 1718 485 13 2 2 6 100 371 12 3 100 679 1 12 2 9 1 29 2 10 1 1-1 2 /kg 1-2 3 1-3 2 http://www.maff.go.jp/ 3 Excel 2 15 1 26 2 2 9 16 1 30 2 10 1-4

More information

F8302D_1目次_160527.doc

F8302D_1目次_160527.doc N D F 830D.. 3. 4. 4. 4.. 4.. 4..3 4..4 4..5 4..6 3 4..7 3 4..8 3 4..9 3 4..0 3 4. 3 4.. 3 4.. 3 4.3 3 4.4 3 5. 3 5. 3 5. 3 5.3 3 5.4 3 5.5 4 6. 4 7. 4 7. 4 7. 4 8. 4 3. 3. 3. 3. 4.3 7.4 0 3. 3 3. 3 3.

More information

Excel97関数編

Excel97関数編 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

More information

calibT1.dvi

calibT1.dvi 1 2 flux( ) flux 2.1 flux Flux( flux ) Flux [erg/sec/cm 2 ] erg/sec/cm 2 /Å erg/sec/cm 2 /Hz 1 Flux -2.5 Vega Vega ( Vega +0.03 ) AB cgs F ν [erg/cm 2 /s/hz] m(ab) = 2.5 logf ν 48.6 V-band 2.2 Flux Suprime-Cam

More information

13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x

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

stat-excel-12.tex (2009 12 8 ) 2 -countif Excel 22 http://software.ssri.co.jp/statweb2/ 1. 111 3 2. 4 4 3 3. E4:E10 E4:E10 OK 4. E4:E10 E4:E10 5 6 2/1

stat-excel-12.tex (2009 12 8 ) 2 -countif Excel 22 http://software.ssri.co.jp/statweb2/ 1. 111 3 2. 4 4 3 3. E4:E10 E4:E10 OK 4. E4:E10 E4:E10 5 6 2/1 stat-excel-12.tex (2009 12 8 ) 1 (Microsoft) (excel) (Sun Microsystems) = (open-office calc) 1 2 3 3 1 3 1 2 3 1 2 3 1/12 stat-excel-12.tex (2009 12 8 ) 2 -countif Excel 22 http://software.ssri.co.jp/statweb2/

More information

... 3... 3... 3... 3... 4... 7... 10... 10... 11... 12... 12... 13... 14... 15... 18... 19... 20... 22... 22... 23 2

... 3... 3... 3... 3... 4... 7... 10... 10... 11... 12... 12... 13... 14... 15... 18... 19... 20... 22... 22... 23 2 1 ... 3... 3... 3... 3... 4... 7... 10... 10... 11... 12... 12... 13... 14... 15... 18... 19... 20... 22... 22... 23 2 3 4 5 6 7 8 9 Excel2007 10 Excel2007 11 12 13 - 14 15 16 17 18 19 20 21 22 Excel2007

More information

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................ 5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)

More information

2 1 17 1.1 1.1.1 1650

2 1 17 1.1 1.1.1 1650 1 3 5 1 1 2 0 0 1 2 I II III J. 2 1 17 1.1 1.1.1 1650 1.1 3 3 6 10 3 5 1 3/5 1 2 + 1 10 ( = 6 ) 10 1/10 2000 19 17 60 2 1 1 3 10 25 33221 73 13111 0. 31 11 11 60 11/60 2 111111 3 60 + 3 332221 27 x y xy

More information

…K…E…X„^…x…C…W…A…fi…l…b…g…‘†[…N‡Ì“‚¢−w‘K‡Ì‹ê™v’«‡É‡Â‡¢‡Ä

…K…E…X„^…x…C…W…A…fi…l…b…g…‘†[…N‡Ì“‚¢−w‘K‡Ì‹ê™v’«‡É‡Â‡¢‡Ä 2009 8 26 1 2 3 ARMA 4 BN 5 BN 6 (Ω, F, µ) Ω: F Ω σ 1 Ω, ϕ F 2 A, B F = A B, A B, A\B F F µ F 1 µ(ϕ) = 0 2 A F = µ(a) 0 3 A, B F, A B = ϕ = µ(a B) = µ(a) + µ(b) µ(ω) = 1 X : µ X : X x 1,, x n X (Ω) x 1,,

More information

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1 I, A 25 8 24 1 1.1 ( 3 ) 3 9 10 3 9 : (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4), (3,3,3) 10 : (1,3,6), (1,4,5), (2,2,6), (2,3,5), (2,4,4), (3,3,4) 6 3 9 10 3 9 : 6 3 + 3 2 + 1 = 25 25 10 : 6 3 + 3 3

More information

Word 2000 Standard

Word 2000 Standard .1.1 [ ]-[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [OK] [ ] 1 .1.2 [ ]-[ ] [ ] [ ] [ [ ] [ ][ ] [ ] [ ] [ / ] [OK] [ ] [ ] [ ] [ ] 2 [OK] [ ] [ ] .2.1 [ ]-[ ] [F5] [ ] [ ] [] [ ] [ ] [ ] [ ] 4 ..1 [ ]-[ ] 5 ..2

More information

最小2乗法,最尤法 線形モデル,非線形モデル

最小2乗法,最尤法    線形モデル,非線形モデル 1 2004. 2. 10 2 0 1 0.1 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 0.2 : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1 2 4 1.1 : : : : : : : : : : : : : : : : : : :

More information

3 4 6 10 11 14 16 19

3 4 6 10 11 14 16 19 PowerPoint2007 3 4 6 10 11 14 16 19 PowerPoint PowerPoint PowerPoint 1 PowerPoint 1 1 2 3 4 5 2 [ ] 3 4 8 1 2 3 5 2 6 1 7 8 Office PowerPoint 2007 9 10 2 3 11 6 12 Ctrl 2 Shift 2 5 2 Shift 5 2 Delete 13

More information

301-A2.pdf

301-A2.pdf 301 21 1 (1),, (3), (4) 2 (1),, (3), (4), (5), (6), 3,?,?,??,?? 4 (1)!?, , 6 5 2 5 6 1205 22 1 (1) 60 (3) (4) (5) 2 (1) (3) (4) 3 (1) (3) (4) (5) (6) 4 (1) 5 (1) 6 331 331 7 A B A B A B A 23 1 2 (1) (3)

More information

「産業上利用することができる発明」の審査の運用指針(案)

「産業上利用することができる発明」の審査の運用指針(案) 1 1.... 2 1.1... 2 2.... 4 2.1... 4 3.... 6 4.... 6 1 1 29 1 29 1 1 1. 2 1 1.1 (1) (2) (3) 1 (4) 2 4 1 2 2 3 4 31 12 5 7 2.2 (5) ( a ) ( b ) 1 3 2 ( c ) (6) 2. 2.1 2.1 (1) 4 ( i ) ( ii ) ( iii ) ( iv)

More information

ネットショップ・オーナー2 ユーザーマニュアル

ネットショップ・オーナー2  ユーザーマニュアル 1 1-1 1-2 1-3 1-4 1 1-5 2 2-1 A C 2-2 A 2 C D E F G H I 2-3 2-4 2 C D E E A 3 3-1 A 3 A A 3 3 3 3-2 3-3 3-4 3 C 4 4-1 A A 4 B B C D C D E F G 4 H I J K L 4-2 4 C D E B D C A C B D 4 E F B E C 4-3 4

More information

EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編

EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編 K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D

More information

ありがとうございました

ありがとうございました - 1 - - 2 - - 3 - - 4 - - 5 - 1 2 AB C A B C - 6 - - 7 - - 8 - 10 1 3 1 10 400 8 9-9 - 2600 1 119 26.44 63 50 15 325.37 131.99 457.36-10 - 5 977 1688 1805 200 7 80-11 - - 12 - - 13 - - 14 - 2-1 - 15 -

More information

EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編

EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編 K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D

More information

公務員人件費のシミュレーション分析

公務員人件費のシミュレーション分析 47 50 (a) (b) (c) (7) 11 10 2018 20 2028 16 17 18 19 20 21 22 20 90.1 9.9 20 87.2 12.8 2018 10 17 6.916.0 7.87.4 40.511.6 23 0.0% 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2.0% 4.0% 6.0% 8.0%

More information

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 A B (A/B) 1 1,185 17,801 6.66% 2 943 26,598 3.55% 3 3,779 112,231 3.37% 4 8,174 246,350 3.32% 5 671 22,775 2.95% 6 2,606 89,705 2.91% 7 738 25,700 2.87% 8 1,134

More information

橡hashik-f.PDF

橡hashik-f.PDF 1 1 1 11 12 13 2 2 21 22 3 3 3 4 4 8 22 10 23 10 11 11 24 12 12 13 25 14 15 16 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 144 142 140 140 29.7 70.0 0.7 22.1 16.4 13.6 9.3 5.0 2.9 0.0

More information

198

198 197 198 199 200 201 202 A B C D E F G H I J K L 203 204 205 A B 206 A B C D E F 207 208 209 210 211 212 213 214 215 A B 216 217 218 219 220 221 222 223 224 225 226 227 228 229 A B C D 230 231 232 233 A

More information

1

1 1 2 3 4 5 (2,433 ) 4,026 2710 243.3 2728 402.6 6 402.6 402.6 243.3 7 8 20.5 11.5 1.51 0.50.5 1.5 9 10 11 12 13 100 99 4 97 14 A AB A 12 14.615/100 1.096/1000 B B 1.096/1000 300 A1.5 B1.25 24 4,182,500

More information

PowerPoint プレゼンテーション

PowerPoint プレゼンテーション 0 1 2 3 4 5 6 1964 1978 7 0.0015+0.013 8 1 π 2 2 2 1 2 2 ( r 1 + r3 ) + π ( r2 + r3 ) 2 = +1,2100 9 10 11 1.9m 3 0.64m 3 12 13 14 15 16 17 () 0.095% 0.019% 1.29% (0.348%) 0.024% 0.0048% 0.32% (0.0864%)

More information

Excelを使ったAHPの計算方法

Excelを使ったAHPの計算方法 Excel 入門 ( その 3) 23 24 (a) (b) (c) (d) 1 Excel 23 Excel Excel Enter 1 2 Tab 1 Enter 2 AHP n n F2 =B2*C2*D2*E2 25 2 4 30 4 4 30 4 1 30 30 4 1 Excel G2 =F2^(1/4)^Excel 26 1 3 Excel F2 G2 G2 3 1 4 3 4 3 27

More information

1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0

1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0 A c 2008 by Kuniaki Nakamitsu 1 1.1 t 2 sin t, cos t t ft t t vt t xt t + t xt + t xt + t xt t vt = xt + t xt t t t vt xt + t xt vt = lim t 0 t lim t 0 t 0 vt = dxt ft dft dft ft + t ft = lim t 0 t 1.1

More information

a-b...

a-b... ,,.... a-b... m m, RC..... a-b, ....,. a-b .......... GHQA.. .,., KK... PHP..... .... a VOL............. b a-b . .......... ,, ,,,........... .... ...... . ,....... ......... ........... ........ ,,kg

More information

2005

2005 20 30 8 3 190 60 A,B 67,2000 98 20 23,600 100 60 10 20 1 3 2 1 2 1 12 1 1 ( ) 340 20 20 30 50 50 ( ) 6 80 5 65 17 21 5 5 12 35 1 5 20 3 3,456,871 2,539,950 916,921 18 10 29 5 3 JC-V 2 ( ) 1 17 3 1 6

More information

24.15章.微分方程式

24.15章.微分方程式 m d y dt = F m d y = mg dt V y = dy dt d y dt = d dy dt dt = dv y dt dv y dt = g dv y dt = g dt dt dv y = g dt V y ( t) = gt + C V y ( ) = V y ( ) = C = V y t ( ) = gt V y ( t) = dy dt = gt dy = g t dt

More information

untitled

untitled 1 BASIC (Beginner s All-purpose Symbolic Instruction Code) EXCEL BASIC EXCEL EXCEL VBA (Visual Basic for Applications) 2 3 1.1 Excel Excel Excel Check Point 1. 2. 1.1.1 Sheet1 A Sheet2 Sheet A A10 4 1

More information

2 1 Mathematica Mathematica Mathematica Mathematica Windows Mac *1 1.1 1.1 Mathematica 9-1 Expand[(x + y)^7] (x + y) 7 x y Shift *1 Mathematica 1.12

2 1 Mathematica Mathematica Mathematica Mathematica Windows Mac *1 1.1 1.1 Mathematica 9-1 Expand[(x + y)^7] (x + y) 7 x y Shift *1 Mathematica 1.12 Chapter 1 Mathematica Mathematica Mathematica 1.1 Mathematica Mathematica (Wolfram Research) Windows, Mac OS X, Linux OS Mathematica 88 2012 11 9 2 Mathematica 2 1.2 Mathematica Mathematica 2 1 Mathematica

More information

抵 抗 値 [Ω] 04.0 累 積 数 頻 度 数 頻 度 分 布 表 市 販 の 00Ωの 抵 抗 の 抵 抗 値 の 分 布 00 00 300 03.5 03.0 0.5 0.0 正 正 正 0.5 0.0 正 正 正 正 正 正 00.5 正 正 正 正 正 正 正 正 00.0 99.5

抵 抗 値 [Ω] 04.0 累 積 数 頻 度 数 頻 度 分 布 表 市 販 の 00Ωの 抵 抗 の 抵 抗 値 の 分 布 00 00 300 03.5 03.0 0.5 0.0 正 正 正 0.5 0.0 正 正 正 正 正 正 00.5 正 正 正 正 正 正 正 正 00.0 99.5 機 械 システム 応 用 実 験 ~データの 統 計 的 処 理 とデータの 考 察 について~ I. データの 統 計 的 処 理 まず データの 統 計 的 処 理 について 学 ぶ ある 物 理 量 を 測 定 する 場 合 測 定 値 の 誤 差 を 考 慮 する 必 要 がある 測 定 値 の 誤 差 には 間 違 い(mistake)や 系 統 的 誤 差 (systematic error)などがあるが

More information

R

R R ) R NTN NTN NTN NTN NTN @ 1. 2. 3. CONTENTS 4. 5. 6. NTN NTN NTN 1. NTN NTN NTN NTN NTN NTN NTN NTN NTN NTN NTN NTN NTN 2. L1 4 -M8 230 4 -M10 8-11 175 260 250 150 210 230 Bpx 150 250 210 Bx Bpx

More information

2 36 41 41 42 44 44 1 2 16 17 18 19 20 25 26 27 28 29 4 4.12 32 4.2 4.2.1 36 4.2.2 41 4.2.3 41 4.2.4 42 4.3 4.3.1 44 4.3.2 44 31 1 32 33 < 2 x 1 x x 2 < x 1 x1x 2 x1x 2 34 36 4.2 (1) (4) (1)

More information

f (x) f (x) f (x) f (x) f (x) 2 f (x) f (x) f (x) f (x) 2 n f (x) n f (n) (x) dn f f (x) dx n dn dx n D n f (x) n C n C f (x) x = a 1 f (x) x = a x >

f (x) f (x) f (x) f (x) f (x) 2 f (x) f (x) f (x) f (x) 2 n f (x) n f (n) (x) dn f f (x) dx n dn dx n D n f (x) n C n C f (x) x = a 1 f (x) x = a x > 5.1 1. x = a f (x) a x h f (a + h) f (a) h (5.1) h 0 f (x) x = a f +(a) f (a + h) f (a) = lim h +0 h (5.2) x h h 0 f (a) f (a + h) f (a) f (a h) f (a) = lim = lim h 0 h h 0 h (5.3) f (x) x = a f (a) =

More information

木オートマトン•トランスデューサによる 自然言語処理

木オートマトン•トランスデューサによる   自然言語処理 木オートマトン トランスデューサによる 自然言語処理 林 克彦 NTTコミュニケーション科学基礎研究所 hayashi.katsuhiko@lab.ntt.co.jp n I T 1 T 2 I T 1 Pro j(i T 1 T 2 ) (Σ,rk) Σ rk : Σ N {0} nσ (n) rk(σ) = n σ Σ n Σ (n) Σ (n)(σ,rk)σ Σ T Σ (A) A

More information

22 22 22 22 22 33 33 33 33 33 44 44 44 44 44 55 55 55 55 55 66 66 66 66 66 88 88 88 88 22 22 3 3 33 4 4 44 44 5 5 55 55 66 66 66 66 77 77 8 8 88 88 33 33 33 44 44 55 55 66 66 77 77 @ 2 2 2 2 2 2 2 2 2

More information

36.fx82MS_Dtype_J-c_SA0311C.p65

36.fx82MS_Dtype_J-c_SA0311C.p65 P fx-82ms fx-83ms fx-85ms fx-270ms fx-300ms fx-350ms J http://www.casio.co.jp/edu/ AB2Mode =... COMP... Deg... Norm 1... a b /c... Dot 1 2...1...2 1 2 u u u 3 5 fx-82ms... 23 fx-83ms85ms270ms300ms 350MS...

More information

a a apier sin 0; 000; 000 = 0 7 sin 0 0; 000; 000 a = 0 7 ;r = 0: = 0 7 a n =0 7 ( 0 7 ) n n =0; ; 2; 3; n =0; ; 2; 3; ; 00 a n+ =0 7 ( 0 7 ) n

a a apier sin 0; 000; 000 = 0 7 sin 0 0; 000; 000 a = 0 7 ;r = 0: = 0 7 a n =0 7 ( 0 7 ) n n =0; ; 2; 3; n =0; ; 2; 3; ; 00 a n+ =0 7 ( 0 7 ) n apier John apier(550-67) 0 2 3 4 5 6 7 8 9 0 2 4 8 6 32 64 28 256 52 024 4 32 = 28 2+5=7 2 n n 2 n 2 m n + m a 0 ;a ;a 2 ;a 3 ; a = a 0 ; r = a =a 0 = a 2 =a = a 3 =a 2 = n a n a n = ar n a r 2 a m = ar

More information

統計的仮説検定とExcelによるt検定

統計的仮説検定とExcelによるt検定 I L14(016-01-15 Fri) : Time-stamp: 016-01-15 Fri 14:03 JST hig 1,,,, p, Excel p, t. http://hig3.net ( ) L14 Excel t I(015) 1 / 0 L13-Q1 Quiz : n = 9. σ 0.95, S n 1 (n 1)

More information

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1) D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y

More information