3 2 expected values of discrete random variables

... 18 Activity 3. 2: Identifying Sources of Information Exercise 1: Identifying Sources of Information ! Develop a list of sources of information Review the information ... the Ferguson and Bardell, Inc case study In the following table, list examples for each source of information You will discuss your results in a class discussion Sources Examples Artifacts Systems...

Ngày tải lên: 24/01/2014, 10:20

... Problems 122 122 122 1 23 124 125 126 127 128 129 161 161 161 161 1 62 165 169 1 72 1 72 209 20 9 20 9 21 0 2 13 2 13 21 6 21 8 21 9 24 7 24 7 24 7 24 7 24 8 24 8 24 9 24 9 25 0 vii Chapter Decision Theory 26 4 8.1 ... 28 1 28 1 28 2 2 83 28 4 28 5 28 5 28 6 Appendix A Normal Distribution 29 7 Appendix B Fourier Transform 29 9 B.1 Continuous-Time Fourier Transform B .2 Discrete- Time Fourier Transform Index 29 9 30 0 30 3 ... Special Distributions 2. 8 Conditional Distributions Solved Problems Chapter Multiple Random Variables 38 38 39 41 41 42 43 48 48 79 3. 1 Introduction 3. 2 Bivariate Random Variables 3. 3 Joint Distribution...

Ngày tải lên: 31/03/2014, 16:25

... 13, 34 3 35 6 (20 00) doi:10.10 23 / A:1007849609 23 4 doi:10.1186/1 029 -24 2X -20 11-76 Cite this article as: Sung: A note on the complete convergence for arrays of dependent random variables Journal of ... Proof Since e−x ≤ − exp x2 8Bn 2Bn 3xy x/(12y) (2 :3) 1 ≤ for x > 0, we get that for x > and y > 0, 1+x x = exp − 3xy 2Bn x/(12y) ≤ 2Bn 3xy x/(12y) (2: 4) We also get that Bn 4(xy + Bn ) x/(12y) ... association of random variables, with applications Ann stat 11, 28 6 29 5 (19 83) doi:10. 121 4/aos/117 634 6079 Lehmann, EL: Some concepts of dependence Ann Math Stat 37 , 1 137 –11 53 (1966) doi:10. 121 4/aoms/117769 926 0...

Ngày tải lên: 20/06/2014, 22:20

... Series A, vol 34 , a pp 121 – 1 32 , 19 72 23 P K Sen, “The impact of Wassily Hoeffding’s research on nonparametric,” in Collected Works of Wassily Hoeffding, N I Fisher and P K Sen, Eds., pp 29 –55, Springer, ... support of the two random variables X and Y These notes and the definitions of A and B given in 15/16 Consequently, bound 2. 5 implies that Proposition 2. 2 imply that − A − B |Cov X, Y | ≤ 15 64 0. 23 4 4, ... no 2, pp 159–166, 20 02 11 S Izumino, J E Peˇ ari´ , and B Tepeˇ , “A Gruss-type inequality and its applications,” Journal of c c s ¨ Inequalities and Applications, vol 20 05, no 3, pp 27 7 28 8, 20 05...

Ngày tải lên: 21/06/2014, 18:20

... associated random variables, Probability and Mathematical Statistics 20 (20 00), no 1, 2 03 21 4 [8] P Matula, Limit theorems for sums of nonmonotonic functions of associated random variables, Journal of ... Planning and Inference 97 (20 01), no 2, 20 1 22 5 [6] J Esary, F Proschan, and D Walkup, Association of random variables, with applications, Annals of Mathematical Statistics 38 (1967), 1466–1474 [7] ... (4 .3) − EY j ) converges to zero almost surely as n → ∞ Proof The proof is an immediate consequence of Theorem 3. 2 and the Kronecker lemma (Chung [3] ) Remark 4 .3 Birkel [2] proved a strong law of...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 13/11/2014, 09:19

... Resources; 12 PhotoEdit, Inc., ©DK Images; 13 Getty Images; 16 eStock Photo; 19 Canali Photobank; 20 The Art Institute of Chicago; 21 Getty Images, The Minneapolis Institute of Art; 23 Getty Images ... to see the head of a man and what looked like the body of a great snake ISBN: 0 - 32 8- 135 37 -2 Copyright © Pearson Education, Inc All Rights Reserved Printed in the United States of America This ... photo by Edward Steichen, invented a new style of sculpture Red Cube by Isama Noguchi 12 13 One of Rodin’s greatest projects consisted of a set of huge bronze doors, on which he worked for seven...

Ngày tải lên: 11/02/2017, 05:23

... look at other works of art by the artists in the book Have them find books in the library or Internet photos Have them share favorite works of art The Inspiration of Art 16 924 _LRD_TG_056-057 57 ... to the preservation of important themes from past artistic styles Main Idea Supporting Details © Pearson Education 58 16 924 _LRD_TG_058_059 1/4/06 9: 42: 00 AM The Inspiration of Art Name Vocabulary ... a paragraph about visiting him, using as many vocabulary words as you can 59 16 924 _LRD_TG_058_059 3/ 20 /06 8:46 :30 AM ...

Ngày tải lên: 11/02/2017, 06:05

... Images; 20 (T) Senckenberg Nature Museum, Frankfurt/DK Images Unless otherwise acknowledged, all photographs are the copyright © of Dorling Kindersley, a division of Pearson ISBN: 0 - 32 8- 138 12- 6 Copyright ... Unless otherwise acknowledged, all photographs are the copyright © of Dorling Kindersley, a division of Pearson trait ISBN: 0 - 32 8- 138 12- 6 vertebrate an animal with a backbone Copyright © Pearson Education, ... insects from long ago 21 How Today’s Animals Compare With Those of Long Ago Fossilized plants 22 Scientists like to study both plant and animal fossils From fossils, scientists can often figure out...

Ngày tải lên: 21/04/2017, 08:51

... k-co2k

Ngày tải lên: 02/07/2014, 20:20

... today? It’s October 10th 20 08 February 20 08 july 20 08 october 10 20 08 november 20 20 08 Matching (Ex WB pages 23 )         a- 1st b- 2nd 1- sixth 2- ninth c- 3rd d- 4th 3- seventh 4- first e- ... numbers first 1st  second 2nd   third 3rd  fourth 4th fifth 5th  sixth 6th  seventh 7th  eighth 8th  twentieth 20 th  twenty-first 21 st  twenty-second 22 nd  thirtieth 30 th   What’s the ... 5- tenth 6- fifth 7- eighth 8- second a-4 b-8 c-10 d-9 e-6 f-1 g -3 h-7 i -2 j-5 Homework Do exrcise ( 12) THE END Warm up: Months of the year January February March April May June July August September...

Ngày tải lên: 29/09/2013, 10:10

... identity of the disappearing bridegroom of Miss Mary Sutherland A professional case of great gravity was engaging my own attention at the time, and the whole of next day I was busy at the bedside of ... had I known him to fail, in the case of the King of Bohemia and of the Irene Adler photograph; but when I looked back to the weird business of 'The Sign of Four', and the extraordinary circumstances ... mean, of course, the loss of a hundred a year, so what does her stepfather to prevent it? He takes the obvious course of keeping her at home and forbidding her to seek the company of people of her...

Ngày tải lên: 29/10/2013, 02:15

... command mode Upon completion of the previous steps, logoff by typing exit Turn the router off 2- 4 CCNA 2: Routers and Routing Basics v 3. 0 - Lab 3. 2. 5 Copyright  20 03, Cisco Systems, Inc Erasing ... Enter The router is ready for the assigned lab to be performed 3- 4 CCNA 2: Routers and Routing Basics v 3. 0 - Lab 3. 2. 5 Copyright  20 03, Cisco Systems, Inc Router Interface Summary Router Ethernet ... that can be used in IOS command to represent the interface 4-4 CCNA 2: Routers and Routing Basics v 3. 0 - Lab 3. 2. 5 Copyright  20 03, Cisco Systems, Inc ...

Ngày tải lên: 24/01/2014, 19:20

... command mode Upon completion of the previous steps, logoff by typing exit Turn the router off 2- 4 CCNA 2: Routers and Routing Basics v 3. 0 - Lab 3. 2. 5 Copyright  20 03, Cisco Systems, Inc Erasing ... Enter The router is ready for the assigned lab to be performed 3- 4 CCNA 2: Routers and Routing Basics v 3. 0 - Lab 3. 2. 5 Copyright  20 03, Cisco Systems, Inc Router Interface Summary Router Ethernet ... that can be used in IOS command to represent the interface 4-4 CCNA 2: Routers and Routing Basics v 3. 0 - Lab 3. 2. 5 Copyright  20 03, Cisco Systems, Inc ...

Ngày tải lên: 24/01/2014, 19:20

... u, |at − 1 |2 2|ρt − 1 |2 + 2t2 2 + ρ2tt2 2 , (10) Nguyen Huu Bao / VNU Journal of Science, Mathematics - Physics 23 (20 07) 70-75 72 we can see |a − 1 |2 = (ρ cos θ − 1 )2 + ( 2 sin2 θ) It follows ... 1) Then N I2 ε C2 T α dz C2 εT α N (22 ) Finally, with α from condition (5), we have µα + µα A A α N By using (19), (20 ), (21 ), ( 23 ) , we conclude that ( 23 ) I3 |ψ(t) − ψ1 (t)| 2 + C2 εT α N + ... µα A A Nα (24 ) 74 Nguyen Huu Bao / VNU Journal of Science, Mathematics - Physics 23 (20 07) 70-75 1 − α Choosing T = ε and N = T = ε 3 , we can see that 1 1− − α C2 εT N C2 ε 3 = C2 ε , − (µα...

Ngày tải lên: 14/03/2014, 13:20

... 20 0 μm 20 0 μm E F BNIP3 β-actin KA CL Ctrl BNIP3 antibody +BNIP3–GST 62 kDa BNIP3 expression (fold) BNIP3 antibody 62 kDa 12 10 ** ** KA BNIP3 KA CL Ctrl Ctrl G H 40 M 40 positively for BNIP3 ... transfected using LipofectAMINE 20 00 with a pcDNA3–hBNIP3 plasmid encoding full-length BNIP3, a pcDNA3–hBNIP3)1 63 plasmid encoding the first 1 63 amino acids of BNIP3, or the empty pcDNA3 plasmid The ... 134 –1 42 ª 20 10 The Authors Journal compilation ª 20 10 FEBS Z Zhang et al BNIP3 in excitotoxicity B A Cell death (%) 80 Glu100 μM Glu10 μM 60 40 20 12 24 Hours 36 48 D C E Glu h h 12 h 24 h 36 ...

Ngày tải lên: 22/03/2014, 17:20

... 4n L∈D L∈D ≤e k4 β 4n k2 β 2n X 2 dX T (L) e− k2 β 2n X 2 dX F =e =e k4 β 4n R k4 β 4n e− k2 β 2n X 2 dX (k−1 )2 2πn βk = ≤ Therefore, e− dX ≥ ≥ k2 n2 ρL 2 2 (k−1 )2 /2 where we have used the ... X k2 n2 ρL −1 n k n Jk − X k ∞ and L − n Jk − X k e− k2 β 2n X 2 T (L) X 2 n k2 k + , −1 n Jk − X k since L − n Jk k 2 − k2 L − ∞ k4 β 4n k2 n2 −βn ·e ρL −1 dX T (L) = e− k4 β 4n −βn ·e k2 n2 ... of contradiction, we may assume without loss of generality (since r < 1) that s1 = and s2 ≥ s3 > Fix ε > and set (s2 − s3 − ε )2 + 4ε(s3 − ε) and ν(ε) = −µ(ε) − ε Let v(ε) = (ε, s2 + µ(ε), s3...

Ngày tải lên: 29/03/2014, 07:20

... Expansion of R as a Taylor series 23 6 Further transformations 23 8 10 Completion of the proof of sufficiency 24 0 11 Proof of the necessity 24 1 12 Completion of the proof 2 43 Chapter 13 Monomial ... Choice of p 22 2 18 Completion of the proof 22 4 Chapter 12 Wide monomial zones of integral normal attraction 22 6 Formulation 22 6 An upper bound for the probability of a large deviation 22 7 Introduction ... Introduction of auxiliary variables 22 9 Study of the basic relation 23 1 Derivation of the fundamental formula 23 2 CONTENTS The fundamental integral formula 23 4 Study of the auxiliary integral 23 5 Expansion...

Ngày tải lên: 08/04/2014, 12:28

... Lemma 2. 1 (iv), and ( 13) , µ 2 2 µ 2 P Vk > + kl(ηk ) = P Vk − EVk > kl(ηk ) 2 2 2 E(Vk − EVk )2 EX I(|X| ≤ ηk ) ≤c ≤c k2 l2 (ηk ) kl2 (ηk ) o(1)ηk = o(1) → = kl(ηk ) 10 ( 23 ) Therefore, from ... Stat Probab Lett 28 1(6), 6 62 6 72 (20 11) [10] Wu, QY: An almost sure central limit theorem for the weight function sequences of NA random variables Proc Math Sci 121 (3) , 36 9 37 7 (20 11) [11] Ye, ... Math Appl 60, 2 639 26 44 (20 10) [ 13] Zhang, Y, Yang, XY: An almost sure central limit theorem for self-normalized products of sums of i.i.d random variables J Math Anal Appl 37 6, 29 –41 (20 11) [14]...

Ngày tải lên: 20/06/2014, 21:20

... doi:10.10 73/ pnas .33 .2. 25 Erdös, P: On a theorem of Hsu and Robbins Ann Math Stat 20 , 28 6 29 1 (1949) doi:10. 121 4/aoms/1177 730 037 Huang et al Journal of Inequalities and Applications 20 11, 20 11: 92 http://www.journalofinequalitiesandapplications.com/content /20 11/1/ 92 ... sequences of pairwise NQD random variables Acta Math Sci Ser B Engl Ed 28 (2) , 26 9 28 1 (20 08) Hsu, PL, Robbins, H: Complete convergence and the law of large numbers Proc Natl Acad Sci USA 33 (2) , 25 31 ... properties of pairwise NQD sequences Acta Math Sinica 45 (3) , 617– 624 (20 02) Chen, PY: On the strong law of Large numbers for pairwise NQD random variables Acta Math Sci 25 (3) , 38 6 39 2 (20 05) Gan,...

Ngày tải lên: 20/06/2014, 22:20