2 probably 3 probability theory probability theory (gàil`ü) , 1:
|
|
|
- なお いさし
- 7 years ago
- Views:
Transcription
1 ( ) ( C) 1 probability probability probable probable probable probable probably probably maybe perhaps possibly likely possibly<maybe perhaps<likely<probably probably ( ) 1 probably = almost surely * ( ) 1 Macmillan Dictionary for Children, Robert B. Costello (Ed.), Simon & Schuster, 2001.
2 2 probably 3 probability theory probability theory (gàil`ü) , 1:
3 ZIP 6 ZIP tar gz π π π {0, 1}- ( 2) {0, 1}- 1 {0, 1}- {0, 1}- {0, 1}- {0, 1}- 4 5 bitmap 6
4 2: CD DVD ( ) ( ) x 2 + y 2 = 1 x 2 + y 2 = {0, 1}- {0, 1}- {0, 1} {0, 1} { }} { { }} { 0, 0,..., 0, 1, 1,..., 1 (1) (1) {0, 1} {0, 1}- {0, 1} {0, 1} /
5 10000 {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} (2) (2) x 2x = 2 ( ) = = x 2 1, x x = {0, 1} {0, 1} < = = {0, 1} {0, 1}- 511/512 ; 1 {0, 1} / ; 2 {0, 1} {0, 1}-
6 4 4.1 {0, 1}- {0, 1}- 1 probability theory 1 1 3: ( ) {0,1} - 1 {0,1} - 1
7 4.2 1/ k 100C k = 100!, k = 0, 1,..., 100 (100 k)! k! 50 ± k=35 100C k = = C k k=35 = = % 50 ± ; ± C k k= = ± C k k= =
8 99.9% ± C k k= % = (3) (PC) (3) PC 7 PC PC / ± % ± % ± % / % 5000 ± % 1 ε > 0 n (1/2) ± ε {0, 1}- {0, 1}- 99.9% ± ± 150 ε > 0 n n 1 (1/2) ± ε 1/2 2 ( 1713 ) p 1 p ε > 0 n p ± ε 1 7 MacBook Pro 2.7GHz Intel Core i7 + Mathematica 9
9 ; n p ± ε 1 (1/4nε 2 ) P ( n ) p < ε 1 1 4nε 2. (4) 4.3 1/2 1/ p p S
10 100 6 S p 10 6 n S/10 6 p ± ε 1 P ( ) S 10 p < ε ε 2, ε = 1/200 P ( S 10 p < 1 ) (5) S = 10 8 {0, 1} S/10 6 (5) S/ % 1/200 p 5.2 (5) 10 8 {0, 1}- ω ω ω 10 8 {0, 1}- ω ω ω {0, 1}- ω {0, 1}- {0, 1}- {0, 1}- {0, 1}- {0, 1}- 8
11 5.3 g : {0, 1} l {0, 1} n, l < n {0, 1} l {0, 1} n l n {0, 1}- l ω {0, 1} l ω l {0, 1}- g(ω ) {0, 1} n g(ω ) ω g(ω ) n ω ω {0, 1} l ω = g(ω ) {0, 1} n S(ω) p 10 6 < {0, 1}- ω ω g : {0, 1} 238 {0, 1} 108 ω {0, 1} 238 (5) ( S(g(ω )) P p 10 6 < 1 ) ( - - (RWS ) 4) ω {0, 1} ω g p {0, 1}- 9 S {0, 1} H. Sugita Monte Carlo method, random number, and pseudorandom number, MSJ Memoirs vol.25 Chapter 2
12 4: RWS g : {0, 1} 238 {0, 1} 108 ( ) ω' ; S(ω) = 10 6 k=1 X(ω 100(k 1)+1,..., ω 100k ), ω = (ω 1,..., ω 10 8) {0, 1} 108, X (ξ 1,..., ξ 100 ) {0, 1} 100 { 1 (ξ1,..., ξ ), X(ξ 1,..., ξ 100 ) = 0 ( ), RWS g : {0, 1} 238 {0, 1} 108 m = 100 N = 10 6 j = log 2 N = = 2m + 2j 10 8 = Nm g : {0, 1} 2m+2j {0, 1} Nm ω = (ω 1,..., ω 2m+2j) {0, 1} 2m+2j x = m+j i=1 2 i ω i, α = m+j i=1 2 i ω m+j+i Z k = (d 1 (x + kα),..., d m (x + kα)) {0, 1} m, k = 1,..., N d i (t) t 0 2 i (0 1) Z k ω g(ω ) = (Z 1,..., Z N ) {0, 1} Nm
13 ω {0, 1} S(g(ω )) = p vs 10 PC
14 ; probability mathematics µαθηµατικóς ( )
x : = : x x
x : = : x x x :1 = 1: x 1 x : = : x x : = : x x : = : x x ( x ) = x = x x = + x x = + + x x = + + + + x = + + + + +L x x :1 = 1: x 1 x ( x 1) = 1 x 2 x =1 x 2 x 1= 0 1± 1+ 4 x = 2 = 1 ± 5 2 x > 1
●70974_100_AC009160_KAPヘ<3099>ーシス自動車約款（11.10）.indb
" # $ % & ' ( ) * +, -. / 0 1 2 3 4 5 6 7 8 9 : ; < = >? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y " # $ % & ' ( ) * + , -. / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B
- 1 - - 2 - 320 421 928 1115 12 8 116 124 2 7 4 5 428 515 530 624 921 1115 1-3 - 100 250-4 - - 5 - - 6 - - 7 - - 8 - - 9 - & & - 11 - - 12 - GT GT - 13 - GT - 14 - - 15 - - 16 - - 17 - - 18 - - 19 - -
~ ~.86 ~.02 ~.08 ~.01 ~.01 ~.1 6 ~.1 3 ~.01 ~.ω ~.09 ~.1 7 ~.05 ~.03 ~.01 ~.23 ~.1 6 ~.01 ~.1 2 ~.03 ~.04 ~.01 ~.1 0 ~.1 5 ~.ω ~.02 ~.29 ~.01 ~.01 ~.11 ~.03 ~.02 ~.ω 本 ~.02 ~.1 7 ~.1 4 ~.02 ~.21 ~.I
MultiWriter 5600C 活用マニュアル
1 *1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 9 1 2 3 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 a b c 26 27 28 C *1 *2 *2 29 2 2 2 2 2 2 2 2 2 30 *1 *2 ± *1 C C 31 32 33 34 35 36 M C Y K 1 2 3 4 5 6
204 / CHEMISTRY & CHEMICAL INDUSTRY Vol.69-1 January 2016 047
9 π 046 Vol.69-1 January 2016 204 / CHEMISTRY & CHEMICAL INDUSTRY Vol.69-1 January 2016 047 β γ α / α / 048 Vol.69-1 January 2016 π π π / CHEMISTRY & CHEMICAL INDUSTRY Vol.69-1 January 2016 049 β 050 Vol.69-1
1 1 2 65
3 3 2000 6 14 2 30 4 2 1 1 2 65 1!?? < > 3 2 2 100 19 19 100 100 100 < > 19 2 2 2 2 < > 2000 2000 50 1945 5 50 1945 5 45 20 20 4 1945 4 5 5 5 100 50 20 5 2 20 5 20 5 5 6 20 6 19 5 5 6 5 6 2 20 6 21
untitled
Y = Y () x i c C = i + c = ( x ) x π (x) π ( x ) = Y ( ){1 + ( x )}( 1 x ) Y ( )(1 + C ) ( 1 x) x π ( x) = 0 = ( x ) R R R R Y = (Y ) CS () CS ( ) = Y ( ) 0 ( Y ) dy Y ( ) A() * S( π ), S( CS) S( π ) =
... 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
330
330 331 332 333 334 t t P 335 t R t t i R +(P P ) P =i t P = R + P 1+i t 336 uc R=uc P 337 338 339 340 341 342 343 π π β τ τ (1+π ) (1 βτ )(1 τ ) (1+π ) (1 βτ ) (1 τ ) (1+π ) (1 τ ) (1 τ ) 344 (1 βτ )(1
Title 疑似乱数生成器の安全性とモンテカルロ法 ( 確率数値解析に於ける諸問題,VI) Author(s) 杉田, 洋 Citation 数理解析研究所講究録 (2004), 1351: Issue Date URL
Title 疑似乱数生成器の安全性とモンテカルロ法 ( 確率数値解析に於ける諸問題,VI) Author(s) 杉田, 洋 Citation 数理解析研究所講究録 (2004), 1351: 33-40 Issue Date 2004-01 URL http://hdlhandlenet/2433/64973 Right Type Departmental Bulletin Paper Textversion
http://banso.cocolog-nifty.com/ 100 100 250 5 1 1 http://www.banso.com/ 2009 5 2 10 http://www.banso.com/ 2009 5 2 http://www.banso.com/ 2009 5 2 http://www.banso.com/ < /> < /> / http://www.banso.com/
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%)
H28.4 / 11 28 7 1 28 28 1 27 29 30 4 1 29 5 5 2 2 1 2 2 28 3 1 28 http://www.city.saitama.jp/005/001/018/003/p036471.html 2 28 7 11 28 8 31 3 CD DVD 4 4 5 7 11 8 31 9 1 9 30 10 1 10 31 11 1 11
2
1 2 10 14 945 3000 2012 3 10 4 5 6 7 8 9 10 11 12 2011 11 21 12301430 (1215 ) 13 6 27 17 () ( ) ( ) (112360) 2 (1157) (119099) ((11861231) )( ) (11641205) 3 (1277) 3 4 (1558) (1639)() 12 (1699)( ) 7 (1722)
n=360 28.6% 34.4% 36.9% n=360 2.5% 17.8% 19.2% n=64 0.8% 0.3% n=69 1.7% 3.6% 0.6% 1.4% 1.9% < > n=218 1.4% 5.6% 3.1% 60.6% 0.6% 6.9% 10.8% 6.4% 10.3% 33.1% 1.4% 3.6% 1.1% 0.0% 3.1% n=360 0% 50%
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
MacOSX印刷ガイド
3 CHAPTER 3-1 3-2 3-3 1 2 3 3-4 4 5 6 3-5 1 2 3 4 3-6 5 6 3-7 7 8 3-8 1 2 3 4 3-9 5 6 3-10 7 1 2 3 4 3-11 5 6 3-12 7 8 9 3-13 10 3-14 1 2 3-15 3 4 1 2 3-16 3 4 5 3-17 1 2 3 4 3-18 1 2 3 4 3-19 5 6 7 8
荳也阜轣ｽ螳ｳ蝣ｱ蜻・indd
1 2 3 CHAPTER 1 4 CHAPTER 1 5 6CHAPTER 1 CHAPTER 1 7 8CHAPTER 1 CHAPTER 2 9 10CHAPTER 2 CHAPTER 2 11 12 CHAPTER 2 13 14CHAPTER 3 CHAPTER 3 15 16CHAPTER 3 CHAPTER 3 17 18 CHAPTER 4 19 20CHAPTER 4 CHAPTER
P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22
1 14 28 16 00 17 30 P-1 P-2 P-3 P-4 P-5 2 24 29 17 00 18 30 P-6 P-7 P-8 P-9 P-10 P-11 P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22 5 24 28 16 00 17 30 P-23
項 目
1 1 2 3 11 4 6 5 7,000 2 120 1.3 4,000 04 450 < > 5 3 6 7 8 9 4 10 11 5 12 45 6 13 E. 7 B. C. 14 15 16 17 18 19 20 21 22 23 8 24 25 9 27 2 26 6 27 3 1 3 3 28 29 30 9 31 32 33 500 1 4000 0 2~3 10 10 34
32 1 7 1 20 ( ) [18 30] [21 00] 2 3 ( ( ) ) ( ) 4 1 2 95 ( 7 3 2 ) 1 2 3 2 a b
![32 1 7 1 20 ( ) [18 30] [21 00] 2 3 ( ( ) ) ( ) 4 1 2 95 ( 7 3 2 ) 1 2 3 2 a b](/thumbs/41/22465094.jpg "32 1 7 1 20 ( ) [18 30] [21 00] 2 3 ( ( ) ) ( ) 4 1 2 95 ( 7 3 2 ) 1 2 3 2 a b")
31 1 7 1 ( ) [18 35] [20 40] 2 3 ( ( ) ) ( ) 4 1 2 1 22 1 2 a b T T A c d 32 1 7 1 20 ( ) [18 30] [21 00] 2 3 ( ( ) ) ( ) 4 1 2 95 ( 7 3 2 ) 1 2 3 2 a b 7 1 ( 34 ) 1 7 2 13 ( ) [18 20] [20 00] 2 4 7 3
no
12 2004.9.3. no.234 2004.9.3. no.234 13 14 2004.9.3. no.234 2004.9.3. no.234 15 16 2004.9.3. no.234 2004.9.3. no.234 17 18 2004.9.3. no.234 19 2004.9.3. no.234 20 2004.9.3. no.234 21 2004.9.3. no.234 22
270万回再生レポート
270 270 2 2 Keynote(Mac) Camtasia PC VIdeo5 Point 2 Point 15 2 Point Point ) (2 2 3 2 3 Point 2 4 3 2 1 OK 100 4 10 20 2 75% Point 4 3 SEX Point SEX SEX SEX 2 SEX Point 2 2500 Point ( 100 Point
Lightブログ_Mikata.qxd
46 Ω 1 3 2 15 Ω 47 6 4 5 7 5 CONTENTS 4 6 8 1 2 3 4 1 12 14 16 18 20 5 6 7 8 9 10 11 2 22 24 26 28 30 34 36 12 38 40 2 3 4 13 42 20 58 14 44 21 60 15 16 17 18 19 46 48 50 52 54 22 23 24 25 64 66 68 72
取扱説明書
ED-601 ED-501 ED-401 2 3 4 23 14 5 6 18 10 7 1 2 6 3 4 8 9 16 16 16 12 1 2 18 10 2 1 5 12 11 1 2 1 2 12 1 2 13 16 14 3 2 4 1 1 2 16 3 4 18 15 1 2 16 2 3 1 1 2 3 18 17 18 22 19 D A C 20 A B 22 B C D 22
JA2008
A1 1 10 vs 3 2 1 3 2 0 3 2 10 2 0 0 2 1 0 3 A2 3 11 vs 0 4 4 0 0 0 0 0 3 6 0 1 4 x 11 A3 5 4 vs 5 6 5 1 0 0 3 0 4 6 0 0 1 0 4 5 A4 7 11 vs 2 8 8 2 0 0 0 0 2 7 2 7 0 2 x 11 A5 9 5 vs 3 10 9 4 0 1 0 0 5
untitled
280 200 5 7,800 6 8,600 28 1 1 18 7 8 2 ( 31 ) 7 42 2 / / / / / / / / / / 1 3 (1) 4 5 3 1 1 1 A B C D 6 (1) -----) (2) -- ()) (3) ----(). ()() () ( )( )( )( ) ( ) ( )( )( )( ) () (). () ()() 7 () ( ) 1
untitled
10 log 10 W W 10 L W = 10 log 10 W 10 12 10 log 10 I I 0 I 0 =10 12 I = P2 ρc = ρcv2 L p = 10 log 10 p 2 p 0 2 = 20 log 10 p p = 20 log p 10 0 2 10 5 L 3 = 10 log 10 10 L 1 /10 +10 L 2 ( /10 ) L 1 =10
2012_05_GLK_cover.indd
c %& r Z \ W W n q & F % % & & % & & % % % & % & % & % & % & % & F F % % % & & & & % & A
™…
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
2012_10_A_cover.indd
c %& r Z \ W n % & & % % & % & & % % % & % & % & & % & % %& % & % & % % % & & & W W W W A
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
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
Q&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
bumon_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
‡o‡P†C‡P‡Q”R„û†^‡P†C‡P‡Q
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Q & A ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
EPSON
B K L & & & & & & & & L & & & & & & & K & & & & & L L L & & & K L L L & & L L L & & & & & & & & & & & & & & & & & & & & & & & & & & & L & K L K & & & & & & & L L & & L & & L L & & & & &
6 30 2005 10 1 65 2,682 00 21.9 481 1 2,776 21.0 15 1,740 00 5.8 107 13.6 40 2025 24.2-0 - -1 - -2 - -3 - -4 - -5 - -6 - -7 - -8- -9 - - 10 - -11 - - 12 - - 13-10 11 59 4 59 3 10 17 - 14 - - 15 - - 16
2014-11.key
2014-11 1 2 3 4 5 7 8 9 10 11 12 PC 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 45 46 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
「東京こどもネット・ケータイヘルプデスク（こたエール）」平成22年度相談実績の概要
734, 35% 62, 11% 84, 16% 530, 26% 235, 11% PC) 396, 73% 579, 28% ) (21 ) 2 3 4 5 6 7 8 9 10 11 12 13 200 150 100 22 182 200 150 100 22 50 54 PC 49 52 PC 50 41 14 17 1 1 4 16 3 6 14 180 250 200 150 235
