实例介绍
【实例简介】
INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering_A. Leon-Garcia，国外的随机课程经典教材，这个文档是课后习题答案
A. Leon-Garcia INSTRUCTORS SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineers 1.6 a)In the first draw the outcome can be black(b)or white (u). If the first draw is black, then the second outcome can be b or w. However if the first draw is white. then the run only contains black balls so the second outcome must be b. Therefore S=0b, bw, ubl In this case all outcomes can be b or Therefore S=1bb, bw, wb, wj c)In part a) the outcome ww cannot occur so Juu=0. In part b) let n be a larg number repetitions of the experiment. The number of times the first outcome is 2 is approximately N/ 3 since the run has one white ball and two black balls. Of these N/3 outcomes approximately 1/2 are also white in the second draw. Thus N/9 if the outcome ult is ww, and thus fww=9. d)In the first cx periment, the outcome of the first draw affects the probability of the outcomes in the second draw. In the second experiment, the outcome of the first draw does not affect the probability of the outcomes in the second draw When the experirnent is performed, either A occurs or it doesn't(i.e. B occurs); thus NA(n)+NB(m)=n in n repetitions of the experiment, and fa(n)+ fB(n) Thus fB(n)=1-fA(n) 1. 8 If A, B, or C occurs, then D occurs. Furthermore since A, B, or C cannot occur simultaneously, in n repetitions of the experiment we have ND(n)=NA(n)+NB(n)+Nc(n) and dividing both sides by n fD(n)=fA(n)+fEin)+ fc(n) <X>n ∑X(7)n>0 11 ∑X()+x(n) <X>n-1+-X(n) <X>n-1+ X(n)-<X o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 A. Leon-Garcia INSTRUCTORS SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineers 1.10 2 2 ikala to los PL>D 3= ~8-<-2“ dam at eceu→中么-a了= Vol :它=2元 =cs2=2c4=2c= 111 3 bud we also a scowl 大 basu Spect lanye-teu soil Q 0 -ks LDO o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-1 Probability, Statistics, and Random Processes for Electrical engineers Chapter 2: Basic Concepts of Probability Theory 2.1 Specifying Random Experiments 21)@=,335438 2 A=52343B=13157时2=5535时 ABD=(3}An3=547 AU(B0 112,3,4,4,33 (A0D=52+3 o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-2 Probability, Statistics, and Random Processes for Electrical Engineers 2.2) The outcome of this experiment consists of a pair of numbers (r, y)where T=number of dots in first toss and y= number of dots in second toss. Therefore, S= set of ordered pairs(c, y) where c, yE(1, 2, 3, 4, 5, 6 which are listed in the table below 1 3 4 5 6 4)(1,5)(1 2(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) 3(3,1)(3,2)(3,3)(3,4)(3,5)(3,6) 4(4,1)(4.2)(43)(44)(45)(46) 5(5,1)(5,2)(5,3)(5,4)(5,5)(5,6) 6(6.1)(62)(63)(64)(65)(66 checkmarks indicate elements of events b) 1234 123456 x123456 x123456 A=N2}2=2k2 B d )B is a subset of A so when B occurs then A also occurs, thus B implies A e)A∩B=2N≤1<63 123456 123456 f)c="number of dots differ by ar 123456 3|v 4 6 Comparing the tables for A and C we see A∩=(3D),c2),(C53),C4) o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-3 Probability, Statistics, and Random Processes for Electrical engineers 2.3 乎.S ②A=53 ,(2,(3)所,(D,6) ±3=E32).3)②(,(),,的 22 (43)明(3,色少()(53,秒2 C0+)(5)2)(90D,2c s)(的),(5 6), 2.4 2 20)(3少(32 2 26x-2)2)39 Y):39(32) x d +2 bagel ow ol seu =0}=(3),e3=)f 大 M 2.5 a) Each testing of a pen has two possible outcomes:“ pen good”(g)or“ pen bad”b. The experiment consists of testing pens until a good pen is found. Therefore each outcome of the experiment consists of a string of“bs” ended by a“g”. We assume that each pen is not put back in the drawer after being tests. Thus S=g, bg, bbg, bbbgi, bbb, b)We now simply record the number of pens tested, so S=[1, 2, 3, 43, 53 c)The outcome now consists of a substring of6's"and one "g"in any order followed by a final "g".S=19g, bgg, gbg, gbbg, bbgg, gbbbg, bgbbg, bbgbg, bbbgg, ybbbbg, bg bbbs, blg 5> d)S={2,3,4,5至4 bbbgbs, bbga] o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual Probability, Statistics, and Random Processes for Electrical engineers 26)@ b b,如o,acb,ba,cbc O A=labe,acs] 3=2abs, 4ba C=tabc, baes @(AUBUC)=iabs acb, cbsb-c3=fcab, bcas ∩B abc e PuBic c ac b. cLa. b 27)A=3号33 ={33 e={12,34,S6? AnB=24121…3 6 月-B u wt wa 3 En=2m: w pos fu ucap-, not vw Hu AAB∩e=5 3(a 2.8 A A03 A n AvB o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-5 Probability, Statistics, and Random Processes for Electrical Engineers If we sketch the events A and b we see that B= AU B. We also see that the intervals corresponding to A and C have no points in common so An C A We also see that(r,s=(r,∞)n(-∞,s=(-∞,r]°n(-∞,s that is C=AC∩B 210)A(au)=(4e (A UB)UC AU(Bve) A N (HAD B 包Au(B0c)=AU8)n(Ae) AUCBAC) ④0B)∩(4vc AUB Au An(Buc)=(408)V(An o) An (BU (AnB)U(AnC) BUC o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual Probability, Statistics, and Random Processes for Electrical engineers 2.11 A implies B B Implies C A implies C SInce a is a and then subset of c since bc is a A then C A))4 subset of a B B A implies B B implies A 212)6AVB=Aa人AnB=Aca自=3 e[3AB==3 AC3 reB tu s e AuB s 3 A BcA A=1 23)5~A3m=aBo3) A B o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 【实例截图】
【核心代码】
INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering_A. Leon-Garcia，国外的随机课程经典教材，这个文档是课后习题答案
A. Leon-Garcia INSTRUCTORS SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineers 1.6 a)In the first draw the outcome can be black(b)or white (u). If the first draw is black, then the second outcome can be b or w. However if the first draw is white. then the run only contains black balls so the second outcome must be b. Therefore S=0b, bw, ubl In this case all outcomes can be b or Therefore S=1bb, bw, wb, wj c)In part a) the outcome ww cannot occur so Juu=0. In part b) let n be a larg number repetitions of the experiment. The number of times the first outcome is 2 is approximately N/ 3 since the run has one white ball and two black balls. Of these N/3 outcomes approximately 1/2 are also white in the second draw. Thus N/9 if the outcome ult is ww, and thus fww=9. d)In the first cx periment, the outcome of the first draw affects the probability of the outcomes in the second draw. In the second experiment, the outcome of the first draw does not affect the probability of the outcomes in the second draw When the experirnent is performed, either A occurs or it doesn't(i.e. B occurs); thus NA(n)+NB(m)=n in n repetitions of the experiment, and fa(n)+ fB(n) Thus fB(n)=1-fA(n) 1. 8 If A, B, or C occurs, then D occurs. Furthermore since A, B, or C cannot occur simultaneously, in n repetitions of the experiment we have ND(n)=NA(n)+NB(n)+Nc(n) and dividing both sides by n fD(n)=fA(n)+fEin)+ fc(n) <X>n ∑X(7)n>0 11 ∑X()+x(n) <X>n-1+-X(n) <X>n-1+ X(n)-<X o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 A. Leon-Garcia INSTRUCTORS SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineers 1.10 2 2 ikala to los PL>D 3= ~8-<-2“ dam at eceu→中么-a了= Vol :它=2元 =cs2=2c4=2c= 111 3 bud we also a scowl 大 basu Spect lanye-teu soil Q 0 -ks LDO o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-1 Probability, Statistics, and Random Processes for Electrical engineers Chapter 2: Basic Concepts of Probability Theory 2.1 Specifying Random Experiments 21)@=,335438 2 A=52343B=13157时2=5535时 ABD=(3}An3=547 AU(B0 112,3,4,4,33 (A0D=52+3 o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-2 Probability, Statistics, and Random Processes for Electrical Engineers 2.2) The outcome of this experiment consists of a pair of numbers (r, y)where T=number of dots in first toss and y= number of dots in second toss. Therefore, S= set of ordered pairs(c, y) where c, yE(1, 2, 3, 4, 5, 6 which are listed in the table below 1 3 4 5 6 4)(1,5)(1 2(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) 3(3,1)(3,2)(3,3)(3,4)(3,5)(3,6) 4(4,1)(4.2)(43)(44)(45)(46) 5(5,1)(5,2)(5,3)(5,4)(5,5)(5,6) 6(6.1)(62)(63)(64)(65)(66 checkmarks indicate elements of events b) 1234 123456 x123456 x123456 A=N2}2=2k2 B d )B is a subset of A so when B occurs then A also occurs, thus B implies A e)A∩B=2N≤1<63 123456 123456 f)c="number of dots differ by ar 123456 3|v 4 6 Comparing the tables for A and C we see A∩=(3D),c2),(C53),C4) o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-3 Probability, Statistics, and Random Processes for Electrical engineers 2.3 乎.S ②A=53 ,(2,(3)所,(D,6) ±3=E32).3)②(,(),,的 22 (43)明(3,色少()(53,秒2 C0+)(5)2)(90D,2c s)(的),(5 6), 2.4 2 20)(3少(32 2 26x-2)2)39 Y):39(32) x d +2 bagel ow ol seu =0}=(3),e3=)f 大 M 2.5 a) Each testing of a pen has two possible outcomes:“ pen good”(g)or“ pen bad”b. The experiment consists of testing pens until a good pen is found. Therefore each outcome of the experiment consists of a string of“bs” ended by a“g”. We assume that each pen is not put back in the drawer after being tests. Thus S=g, bg, bbg, bbbgi, bbb, b)We now simply record the number of pens tested, so S=[1, 2, 3, 43, 53 c)The outcome now consists of a substring of6's"and one "g"in any order followed by a final "g".S=19g, bgg, gbg, gbbg, bbgg, gbbbg, bgbbg, bbgbg, bbbgg, ybbbbg, bg bbbs, blg 5> d)S={2,3,4,5至4 bbbgbs, bbga] o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual Probability, Statistics, and Random Processes for Electrical engineers 26)@ b b,如o,acb,ba,cbc O A=labe,acs] 3=2abs, 4ba C=tabc, baes @(AUBUC)=iabs acb, cbsb-c3=fcab, bcas ∩B abc e PuBic c ac b. cLa. b 27)A=3号33 ={33 e={12,34,S6? AnB=24121…3 6 月-B u wt wa 3 En=2m: w pos fu ucap-, not vw Hu AAB∩e=5 3(a 2.8 A A03 A n AvB o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual 2-5 Probability, Statistics, and Random Processes for Electrical Engineers If we sketch the events A and b we see that B= AU B. We also see that the intervals corresponding to A and C have no points in common so An C A We also see that(r,s=(r,∞)n(-∞,s=(-∞,r]°n(-∞,s that is C=AC∩B 210)A(au)=(4e (A UB)UC AU(Bve) A N (HAD B 包Au(B0c)=AU8)n(Ae) AUCBAC) ④0B)∩(4vc AUB Au An(Buc)=(408)V(An o) An (BU (AnB)U(AnC) BUC o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 Instructor,s solutions manual Probability, Statistics, and Random Processes for Electrical engineers 2.11 A implies B B Implies C A implies C SInce a is a and then subset of c since bc is a A then C A))4 subset of a B B A implies B B implies A 212)6AVB=Aa人AnB=Aca自=3 e[3AB==3 AC3 reB tu s e AuB s 3 A BcA A=1 23)5~A3m=aBo3) A B o 2008 Pearson Education, InC, Upper Saddle River, NJ. All rights reserved This material isis protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to Rights and Permissions Department, Pearson Education, Inc, Upper Saddle River, NJ07458 【实例截图】
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