a. How to start: b. How to continue: c. How to stop: b EAP 2. EAP EAP (expected a posteriori) (posteriori distribution) (θ) MAP (maximum a posteriori)
|
|
- やすはる ことじ
- 7 years ago
- Views:
Transcription
1 LET (pp ) EAP EAP (, 2013) (, 2014) PROX (, 2015) (computer-adaptive testing) EAP (expected a posteriori) Keywords: EAP 1. (, 1996, p. 273; Thissen & Mislevy, 2000, p. 101) 25
2 a. How to start: b. How to continue: c. How to stop: b EAP 2. EAP EAP (expected a posteriori) (posteriori distribution) (θ) MAP (maximum a posteriori) (Bayesian modal) (, 2011, p. 83) MAP (, 2011, p. 82) MAP (maximum likelihood estimation method) MAP (2010, p. 190) (2002, p. 35) MAP (2009, p. 56) (2011, p. 83) EAP (, 2011, p. 85;, 2009, p. 56) 2.1 (2012, p. 39) U A B 1 26
3 U A B B A P(B A) = P(A B) P(A) (1) (1) P(B A) A A B 1 A B A B (1) P(A B) 1 (1) P(B A) P(A) ( : ) P(A B) ( : 52 3 ) ( ) P(B A) = P(A B) : P(A) : = =
4 1 2 1 B A A B 1 U A B A B P(A B) = P(A B) P(B) (2) = = 3 12 = (2) (2) P(A B) P(B) ( : ) P(A B) ( : 52 3 ) ( ) (1) (1) : P(B A) = P(A B) P(A) P(A) P(A B) = P(B A)P(A) (3) 28
5 (2) (2) : P(A B) = P(A B) P(B) P(B) P(A B) = P(A B)P(B) (4) (3) (4) P(A B) (3) : P(A B) = P(B A)P(A) (4) : P(A B) = P(A B)P(B) P(B A)P(A) = P(A B)P(B) (5) (5) P(B) P(A B) (6) P(A B) = P(B A)P(A) P(B) (6) 2.2 (2010, p ) (2012, p ) U H D ( 3) 29
6 D D H U H 3. H D 1 3 A H B D (6) : P(A B) = P(H D) = P(B A)P(A) P(B) P(D H )P(H) P(D) (7) D H i (i = 1, 2, 3,, N) ( 4) H i D D H1 D H2 D H3 D H D HN U H1 H2 H3 H HN 4. H D 2 30
7 4 D H i P(D) = P(D H 1 ) + P(D H 2 ) + P(D H 3 ) + + P(D H N ) (8) (3) P(A B) = P(B A)P(A) (8) P(D H i ) P(A B) P(D) 8 : P(D) = P(D H 1 ) + P(D H 2 ) + P(D H 3 ) + + P(D H N ) P(D H i ) = P(D H i )(H i ) P(D) =P(D H 1 )P(H 1 ) + P(D H 2 )P(H 2 ) + P(D H 3 )P(H 3 ) + + P(D H N )P(H N ) (9) (9) (7) : P(H D) = P(D H)P(H) P(D) P(H i D) = P(D H i )P(H i ) P(D H 1 )P(H 1 ) + P(D H 2 )P(H 2 ) + P(D H 3 )P(H 3 ) + + P(D H N )P(H N ) P(H i D) = P(D H i)p(h i ) N P(D H i )P(H i ) i=1 (10) (10) 31
8 (2002, pp ) P(H i D) = P(D H i )P(H i ) P(D H i )P(H i ) dx (11) (11) P(H i D) D H i P(D H i ) H i D U D H i H i P(H i ) D H i (11) P(D) = (11) P(D H i )P(H i ) P(H i D) P(D H i )P(H i ) (i = 1, 2, 3,..., N) (12) (12) U = H D = 32
9 2.3 EAP EAP EAP (expected a posteriori) i (, 2011, p. 84) (expected value) x 1, x 2,...x n, 2007, p. 234, p. 239;, 2015, p. 97 EAP 2 E(X) Khan Academy (2009) 6 2, 2, 3, 5, 5, 6 U ( ) 6 = 3.8 (13) (13) % (2)2 + 1(3) + 2(5) + 1(6) 6 = 1 6 ( ) = = = 33% % % % 6 (14) = =
10 (14) X P(X = x) (x = 1, 2, 3,..., n) E(X) E(X) = n x i p i i=1 (15) E(X) E(X) = x f (x) dx (16) (11) (11) : P(H i D) = P(D H i )P(H i ) P(D H i )P(H i ) dx (11) P(D H i ) likelihood L P(H i D) = L(D H i )P(H i ) L(D H i )P(H i ) dx (17) E(X) (16) (17) θ P(H) g(θ) E(θ i D) = = θ i f (θ i ) dθ i θ i L(D θ i ) g(θ i ) L(D θ i ) g(θ i ) dθ i = θ i L(D θ i ) g(θ i ) L(D θ i ) g(θ i ) dθ i (18) (18) D (2011, p. 85) EAP (5.19) 34
11 N P(X) (maximum likelihood estimation) (2002, pp ) 3 1 n 2 n θ i 3 n 1 I(θ) I(θ) V[ˆθ i θ i ] = 1 I(θ i ) V[ˆθ i θ i ] θ i ˆθ i 3 (2002, p.65) I(θ i ) = E ( ) 2 θ log L (u i θ) θ=θ i (19) (19) I(θ) 1 I(θ) 1 I(θ) I(θ) I(θ) I(θ) 35
12 3.2 X(x i = x 1, x 2, x 3,..., x N ) θ No. x i 1 x 1 P(X = x 1 ; θ) 2 x 2 P(X = x 2 ; θ) 3 x 3 P(X = x 3 ; θ)... N x N P(X = x N ; θ) x 1, x 2, x 3,..., x N P(x i ; θ) P(x i ; θ) = P(X = x 1 ; θ) P(X = x 2 ; θ) P(X = x 3 ; θ) P(X = x N ; θ) (20) (20) θ L(θ ; X = x 1, x 2, x 3,..., x N ) = P(X = x 1, x 2, x 3,..., x N ; θ) (21) L(θ ; X = x 1, x 2, x 3,..., x N ) θ, 2010 (2010, p. 62) (21) L(θ ; x i ) P(x i ; θ) x i θ L(θ ; x i ) N x 1, x 2, x 3,..., x N θ L( x i ) x θ L(θ ; x i ) (20) N log L(θ ; x 1, x 2, x 3,..., x N ) (22) 36
13 L(θ ; x 1, x 2, x 3,..., x N ) θ (, 2007, pp ) U(θ ; x i ) = θ log L (θ ; x i ) (23) E [U(θ ; x i )] (24) (24) 0 (, 2011, p.14) = [ 2 ] [ 2 ] Var [U(θ ; x i )] = E [U(θ ; x i ) 2 ] (E [U(θ ; x i )]) 2 0 (E [U(θ ; x)]) 2 = 0 Var [U(θ ; x i )] = E [U(θ ; x i ) 2 ] (25) U(θ ; x i ) (25) (26) I(θ) (2002, p. 65) (18) (2002) x i θ Var [U(θ ; x i )] = E [U(θ ; x i ) 2 ] = E I(θ) = E ( ( ) 2 θ log L (θ ; x i) ) 2 θ log L (θ ; x i) (26) 37
14 (2002, p. 66) j θ i 2002, pp I j (θ i ) = a 2 p j (θ i ) q j (θ i ) (27) 2 I j (θ i ) = a 2 j p j (θ i ) q j (θ i ) (28) 3 I j (θ i ) = a2 j (p j(θ i ) c j ) 2 q j (θ i ) p j (θ i ) (1 c j ) 2 (29) 1 2 3, 2002, p. 69, 2007, p. 272 I(θ) = b 4. EAP 38
15 (2010).. Khan Academy. (2009, February 24). Expected Value: E(x). [Video file]. Retrieved from Kredt7vY (2011). 8. (1996).. (2007). (2013) Retrieved from Sumi.pdf (2014). 1PLM, 2PLM, 3PLM Retrieved from Sumi.pdf (2015). PROX Retrieved from Sumi.pdf (2002).. (2009). e. (2010). Excel. (2012).!. 39
特許侵害訴訟における無効の主張を認めた判決─半導体装置事件−
[*1847] 12 4 11 10 364 54 4 1368 1710 68 1032 120 X Y 6.8.31 29 3 875 X Y 9.9.10 29 3 819 Y 320275 391468 46 12 21 35 2 6 3513745 39 1 30 320249 1) 1 39 1 [*1848] 2) 3) Y 10 51 2 4 39 5 39 1 3 139 7 2
More informationはじめにお読みください
START 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 & @ 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 & 60 61 62 63 64 65 66 67 68
More informationチュートリアル:ノンパラメトリックベイズ
{ x,x, L, xn} 2 p( θ, θ, θ, θ, θ, } { 2 3 4 5 θ6 p( p( { x,x, L, N} 2 x { θ, θ2, θ3, θ4, θ5, θ6} K n p( θ θ n N n θ x N + { x,x, L, N} 2 x { θ, θ2, θ3, θ4, θ5, θ6} log p( 6 n logθ F 6 log p( + λ θ F θ
More informationTaro13-第6章(まとめ).PDF
% % % % % % % % 31 NO 1 52,422 10,431 19.9 10,431 19.9 1,380 2.6 1,039 2.0 33,859 64.6 5,713 10.9 2 8,292 1,591 19.2 1,591 19.2 1,827 22.0 1,782 21.5 1,431 17.3 1,661 20.0 3 1,948 1,541 79.1 1,541 79.1
More information10:30 12:00 P.G. vs vs vs 2
1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B
More information表1_表4
HN- 95 HN- 93 HN- 90 HN- 87 HN- 85 HN- 82 HN- 80 HN- 77 HN- 75 HN- 72 HN- 70 HN- 67 HN- 65 HN- 60 HN- 55 HN- 50 HN- 45 HN- 40 HN- 35 HN- 30 HN- 25 HN- 20 HN- 15 HN- 10 H02-80H H02-80L H02-70T H02-60H H05-60F
More informationuntitled
146,650 168,577 116,665 122,915 22,420 23,100 7,564 22,562 140,317 166,252 133,581 158,677 186 376 204 257 5,594 6,167 750 775 6,333 2,325 298 88 5,358 756 1,273 1,657 - - 23,905 23,923 1,749 489 1,309
More informationendo.PDF
MAP 18 19 20 21 3 1173 MAP 22 700800 106 3000 23 24 59 1984 358 358 399 25 12 8 1996 3 39 24 20 10 1998 9,000 1,400 5,200 250 12 26 4 1996 156 1.3 1990 27 28 29 8 606 290 250 30 11 24 8 1779 31 22 42 9
More information土壌環境行政の最新動向(環境省 水・大気環境局土壌環境課)
201022 1 18801970 19101970 19201960 1970-2 1975 1980 1986 1991 1994 3 1999 20022009 4 5 () () () () ( ( ) () 6 7 Ex Ex Ex 8 25 9 10 11 16619 123 12 13 14 5 18() 15 187 1811 16 17 3,000 2241 18 19 ( 50
More informationsyuryoku
248 24622 24 P.5 EX P.212 2 P271 5. P.534 P.690 P.690 P.690 P.690 P.691 P.691 P.691 P.702 P.702 P.702 P.702 1S 30% 3 1S 3% 1S 30% 3 1S 3% P.702 P.702 P.702 P.702 45 60 P.702 P.702 P.704 H17.12.22 H22.4.1
More information取扱説明書[NE-202]
NE-202 13.3 m m 1 2 3 m 4 5 6 7 a a a 8 9 10 11 12 a a a a 13 14 15 16 17 2.4 FH 1/XX 4 18 19 20 21 22 23 24 25 26 27 1 2 3 4 5 6 m 7 h 8 r 9 a P b c d e f g h i j ud k l m n o 28 29 30 31 32 33 34 35
More information日経テレコン料金表(2016年4月)
1 2 3 4 8,000 15,000 22,000 29,000 5 6 7 8 36,000 42,000 48,000 54,000 9 10 20 30 60,000 66,000 126,000 166,000 50 100 246,000 396,000 1 25 8,000 7,000 620 2150 6,000 4,000 51100 101200 3,000 1,000 201
More information122011pp.139174 18501933
122011pp.139174 18501933 122011 1850 3 187912 3 1850 8 1933 84 4 1871 12 1879 5 2 1 9 15 1 1 5 3 3 3 6 19 9 9 6 28 7 7 4 1140 9 4 3 5750 58 4 3 1 57 2 122011 3 4 134,500,000 4,020,000 11,600,000 5 2 678.00m
More information2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226. 1893 B pp. 1 2. p. 3.
1 73 72 1 1844 11 9 1844 12 18 5 1916 1 11 72 1 73 2 1862 3 1870 2 1862 6 1873 1 3 4 3 4 7 2 3 4 5 3 5 4 2007 p. 117. 2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226.
More informationMicrosoft Word - 映画『東京裁判』を観て.doc
1 2 3 4 5 6 7 1 2008. 2 2010, 3 2010. p.1 4 2008 p.202 5 2008. p.228 6 2011. 7 / 2008. pp.3-4 1 8 1 9 10 11 8 2008, p.7 9 2011. p.41 10.51 11 2009. p. 2 12 13 14 12 2008. p.4 13 2008, p.7-8 14 2008. p.126
More information73 p.1 22 16 2004p.152
1987 p.80 72 73 p.1 22 16 2004p.152 281895 1930 1931 12 28 1930 10 27 12 134 74 75 10 27 47.6 1910 1925 10 10 76 10 11 12 139 p.287 p.10 11 pp.3-4 1917 p.284 77 78 10 13 10 p.6 1936 79 15 15 30 80 pp.499-501
More information29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23
29 2011 3 pp.55 86 19 1886 2 13 1 1 21 1888 1 13 2 3,500 3 5 5 50 4 1959 6 p.241 21 1 13 2 p.14 1988 p.2 21 1 15 29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23 1
More information() L () 20 1
() 25 1 10 1 0 0 0 1 2 3 4 5 6 2 3 4 9308510 4432193 L () 20 1 PP 200,000 P13P14 3 0123456 12345 1234561 2 4 5 6 25 1 10 7 1 8 10 / L 10 9 10 11 () ( ) TEL 23 12 7 38 13 14 15 16 17 18 L 19 20 1000123456
More information308 ( ) p.121
307 1944 1 1920 1995 2 3 4 5 308 ( ) p.121 309 10 12 310 6 7 ( ) ( ) ( ) 50 311 p.120 p.142 ( ) ( ) p.117 p.124 p.118 312 8 p.125 313 p.121 p.122 p.126 p.128 p.156 p.119 p.122 314 p.153 9 315 p.142 p.153
More information戦後の補欠選挙
1 2 11 3 4, 1968, p.429., pp.140-141. 76 2005.12 20 14 5 2110 25 6 22 7 25 8 4919 9 22 10 11 12 13 58154 14 15 1447 79 2042 21 79 2243 25100 113 2211 71 113 113 29 p.85 2005.12 77 16 29 12 10 10 17 18
More informationDSGE Dynamic Stochastic General Equilibrium Model DSGE 5 2 DSGE DSGE ω 0 < ω < 1 1 DSGE Blanchard and Kahn VAR 3 MCMC 2 5 4 1 1 1.1 1. 2. 118
7 DSGE 2013 3 7 1 118 1.1............................ 118 1.2................................... 123 1.3.............................. 125 1.4..................... 127 1.5...................... 128 1.6..............
More information2012_05_GLK_cover.indd
c %& r Z \ W W n q & F % % & & % & & % % % & % & % & % & % & % & F F % % % & & & & % & A
More informationEPSON
B K L & & & & & & & & L & & & & & & & K & & & & & L L L & & & K L L L & & L L L & & & & & & & & & & & & & & & & & & & & & & & & & & & L & K L K & & & & & & & L L & & L & & L L & & & & &
More information2.8% 2.0% 2.4% 2.4% 0.4% 0.1% 0.3% 0.5% 3.8% 5.6% 25.6% 29.3% 64.6% 60.0% 1
2.8% 2.0% 2.4% 2.4% 0.4% 0.1% 0.3% 0.5% 3.8% 5.6% 25.6% 29.3% 64.6% 60.0% 1 16 24 21 20 20 23 10 11 9 10 3 3 3 2 3 1 3 4 6 8 2 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 3 4 Q & A Q1 A1 Q2 A2 Q3 A3 7
More informationQ&A最低資本金特例030131.PDF
& 1 2 2 3 2 2 3 2 2 3 10 11 10 90 12 13 14 15 16 17 18 19 20 2 2 3 21 2 2 3 22 23 24 25 20 10 26 27 28 10 8 1 29 30 10 8 2 31 32 2 2 3 33 10 8 3 10 11 2 34 10 8 3 10 12 2 35 36 20 10 37 38 39 40 41 42
More information™…
2/10 15 2010. No1362 1 1 216315 91430 Q A & 0.23% 1 1.4% 04-7120-2020 050-5540-2023 Q A & 1 1 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 1 1 2 3 4 5 6 7 8 9 10
More informationbumon_pro.indd
q w e r t y u i o!0 !1!2!3 !4!5!6 !7!8!9 @0 @1 @2 @3 @4 @5 @6 @7 @8 @9 #0 #1 #2 #3 #4 #5 #6 #7 #8 #0 $0 $1 $2 $3 $4 $5 $6 $7 $8 $9 %0 %1 %2 %3 %4 %5 %6 %7 %8 %9 ^0 ^1 ^2 ^3 ^4 ^5 ^6 ^7 ^8 ^9 &0 &1 &2
More information2012_10_A_cover.indd
c %& r Z \ W n % & & % % & % & & % % % & % & % & & % & % %& % & % & % % % & & & W W W W A
More information‡o‡P†C‡P‡Q”R„û†^‡P†C‡P‡Q
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Q & A ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
More informationPart. 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™…{,
16:30-17:40 1-36 1-37 1-38 1-39 1-40 1-41 1-42 33 10:00-11:10 1-43 1-44 1-45 1-46 1-47 1-48 1-49 12:00-12:50 LS4 34 16:30-17:40 1-50 1-51 1-52 1-53 1-54 1-55 1-56 35 16:30-17:40 1-57 1-58 1-59 1-60 1-61
More information59...ec6
No.59 2012 1 SIV SIV SIV HA NA PB1 PB2 PA NP M NS (H3N2) SIV (H1N1) SIV (H1N1) (H3N2) (H1N1) H1N2 H3N2 H1N2 H1N1 SIV (H1N1)2009 2 Proc Jpn Pig Vet Soc No.59 2012 No.59 2012 3 4 Proc Jpn Pig Vet Soc No.59
More information1970:51 1987 1990 1980 1990 1987-2-
Uryu Yoshimitsu 1995:14 :124 1995:295 1979:73-82 -1- 1970:51 1987 1990 1980 1990 1987-2- -3-1 1960 1 2 2 1963 1964 56 1998 1973 1991 1960 1967:1-70 3 1973 1991:196 :112-4- :108 1960 1967 1957 1959 1985:87
More information科技表紙PDF200602
Science & Technology Trends February 2006 1 1 Science & Technology Trends February 2006 11 2 12 3 Science & Technology Trends February 2006 13 14 4 Science & Technology Trends February 2006 15 16 Science
More information01_33.._.c...[.q4.._001-028
EX NHK EX NHK Tonalität einfarbige Blätter ASUKA ASUKA DX EX E E pp. - NHK EX p. p. pp. - EX p. p. p. EX p. p. p. p. p. P.M. p. pp. - p. p. EX p. p. ) p. p. ) - p. delineate p. p. pp. - p.
More information2 1 Introduction
1 24 11 26 1 E-mail: toyoizumi@waseda.jp 2 1 Introduction 5 1.1...................... 7 2 8 2.1................ 8 2.2....................... 8 2.3............................ 9 3 10 3.1.........................
More information80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x
80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = n λ x i e λ x i! = λ n x i e nλ n x i! n n log l(λ) = log(λ) x i nλ log( x i!) log l(λ) λ = 1 λ n x i n =
More information情報理論 第5回 情報量とエントロピー
5 () ( ) ( ) ( ) p(a) a I(a) p(a) p(a) I(a) p(a) I(a) (2) (self information) p(a) = I(a) = 0 I(a) = 0 I(a) a I(a) = log 2 p(a) = log 2 p(a) bit 2 (log 2 ) (3) I(a) 7 6 5 4 3 2 0 0.5 p(a) p(a) = /2 I(a)
More informationtokei01.dvi
2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN
More information[RP13]シリーズカタログ
131520 : : : 2AAWG#24 : 2AAWG#22 1315 : AC30VDC42V 20 : AC100VDC140V 1. 1315 : 15m 20 : 30m DC1A -10 ~ +60-10 ~ +60 2. 1000M DC250V 3. AC300V1 4. 10s 10~55Hz/0.75mm 32 5. 10s 490m/s 2 11ms33 6. 7. 1315
More informationMicrosoft 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 information2
1 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234
More information名称未設定
2007 12 19 i I 1 1 3 1.1.................... 3 1.2................................ 4 1.3.................................... 7 2 9 2.1...................................... 9 2.2....................................
More information浜松医科大学紀要
On the Statistical Bias Found in the Horse Racing Data (1) Akio NODA Mathematics Abstract: The purpose of the present paper is to report what type of statistical bias the author has found in the horse
More information( ) (, ) arxiv: hgm OpenXM search. d n A = (a ij ). A i a i Z d, Z d. i a ij > 0. β N 0 A = N 0 a N 0 a n Z A (β; p) = Au=β,u N n 0 A
( ) (, ) arxiv: 1510.02269 hgm OpenXM search. d n A = (a ij ). A i a i Z d, Z d. i a ij > 0. β N 0 A = N 0 a 1 + + N 0 a n Z A (β; p) = Au=β,u N n 0 A-. u! = n i=1 u i!, p u = n i=1 pu i i. Z = Z A Au
More information中川0119
3 1.4 2. 2-1.6 2-2.9 2-3.9 1.12 1. 51 15 2.19 3.21 4.22 5.25 1.26 2.26 3. 3-1.26 3-2.29 3-3. 3-3-1.30 3-3-2.31 3-3-3.35 3-4.38 3-5.41 4. 4-1.43 4-2.43 1 45 47 48 49 53 57 61 64 67 2 20 30 1 1 6 1 6 1 2008
More information2
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 3 01 02 03 4 04 05 06 5 07 08 09 6 10 11 12 7 13 14 15 8 16 17 18 9 19 20 21 10 22 23 24 11 FIELD MAP 12 13 http://www.pref.ishikawa.jp/shinrin/zei/index.html
More information釧路市幼児教育振興計画(完成版).doc
17 18 10 17 20 29 10 15 19 9,762 9,151 611 29 19 1,842 20 19 3,980 2,706 68 100 1,841 90 17 10 89 44 19 3,560 2,563 72 19 () () () 29 3,980 2,706 67.99 26 1,855 1,841 99.25 55 5,835 4,547 77.93 15
More informationii : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 27 (1) Excel : : : : : : : : : : : : : : : : : : : : : :
i 2006. 4. 11 Excel JMP 0 1 1 (ICC) 2 1.1 2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 (1) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
More informationz z x = y = /x lim y = + x + lim y = x (x a ) a (x a+) lim z z f(z) = A, lim z z g(z) = B () lim z z {f(z) ± g(z)} = A ± B (2) lim {f(z) g(z)} = AB z
Tips KENZOU 28 6 29 sin 2 x + cos 2 x = cos 2 z + sin 2 z = OK... z < z z < R w = f(z) z z w w f(z) w lim z z f(z) = w x x 2 2 f(x) x = a lim f(x) = lim f(x) x a+ x a z z x = y = /x lim y = + x + lim y
More information卓球の試合への興味度に関する確率論的分析
17 i 1 1 1.1..................................... 1 1.2....................................... 1 1.3..................................... 2 2 5 2.1................................ 5 2.2 (1).........................
More informationDocuPrint C2424 取扱説明書(詳細編)
3 4 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1.1 1 1 2 3 4 5 30 1.2 1 31 1.3 1 32 33 1 1.4 1 1.4.1 34 1.4.2 1 2 35 1 1.5 1 1 2 3 4 36 5 6 7 8 9 37 1 1 10 11 12 13 38 14 15
More information