Applied Finite Mathematics
b b
Tomastik/Epstein
,AppliedbFinitebMathematics,bSecondbEdition ©1994,b2008bBrooks/Cole,bCengageb Learning
EdmondbC.bTomastik,bUniversitybofbConnecticut ALLbRIGHTSbRESERVED.bNobpartbofbthisbworkbcoveredbbybthebcopyrightb h
bJanicebL.bEpstein,bTexasbA&MbUniversity ereinbmaybbebreproduced,btransmitted,bstored,borbusedbinbanybformborbbyban
yb meansbgraphic,belectronic,borbmechanical,bincludingbbutbnotblimitedbtobpho
Editor:b CarolynbCrockett
to-
EditorialbAssistant:bRebeccabDashiellb b copying,brecording,bscanning,bdigitizing,btaping,bWebbdistribution,binformatio
MarketingbManager:bMyriahbFitzgibbon nb networks,borbinformationbstoragebandbretrievalbsystems,bexceptbasbpermitt
bTechnicalbEditor:bMarybKanablebIllustr edb underb Sectionb 107b orb 108b ofb theb 1976b Unitedb Statesb Copyrightb Act,b
ator:bJenniferbTribblebPhotographs:bJa withoutb thebpriorbwrittenbpermissionbofbthebpublisher.
nicebEpstein
Forb productb informationb andb technologyb assistance,b contactbusb at
Cengageb Learningb Customerb &b Salesb Support,b 1-800-354-9706.
Forbpermissionbtobusebmaterialbfrombthisbtextborbproduct,bsubmitballb req
uestsbonlinebatbcengage.com/permissions.
Furtherb permissionsb questionsb canb beb e-mailedb to
.
LibrarybofbCongressbControlbNumber:b2008927157
b ISBN-13:b978-0-495-55533-9
ISBN-10:b 0-495-55533-9
Brooks/Cole
10bDavisbDrive
Belmont,bCAb94002-
3098b USA
CengagebLearningbisbableadingbproviderbofbcustomizedblearningbsolutionsbwit
hb officeblocationsbaroundbthebglobe,bincludingbSingapore,bthebUnitedbKingdo
m,b Australia,bMexico,bBrazil,bandbJapan.b Locatebyourblocalbofficebat:bintern
a-b tional.cengage.com/region.
CengagebLearningbproductsbarebrepresentedbinbCanadabbyb Ne
lsonbEducation,bLtd.
Forbyourbcoursebandblearningbsolutions,bvisitbacademic.cengage.com
.b Purchasebanybofbourbproductsbatbyourblocalbcollegebbookstoreborbatb
ourb preferredbonlinebstorebwww.ichapters.com.
PrintedbinbthebUnitedbStatesbofbAmerica
b 1 b2 b3 b4 b5 b6 b7b 12b 11b 10b 09b 08
,Contents
Preface iv
L Logic 2
L.1 IntroductionbtobLogicb .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b . 3
L.2 TruthbTablesb .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b . 8
1 SetsbandbProbability 12
1.1 IntroductionbtobSets ............................................................................ 13
1.2 ThebNumberbofbElementsbinbabSet ....................................................... 22
1.3 SamplebSpacesbandbEvents ................................................................. 29
1.4 BasicsbofbProbability........................................................................... 37
1.5 RulesbforbProbability........................................................................... 44
1.6 ConditionalbProbability ...................................................................... 53
1.7 Bayes’bTheorem ................................................................................. 66
Review ............................................................................................... 74
2 CountingbandbProbability 82
2.1 ThebMultiplicationbPrinciplebandbPermutations .................................. 83
2.2 Combinations ..................................................................................... 93
2.3 ProbabilitybApplicationsbofbCountingbPrinciples............................... 100
2.4 BernoullibTrials ................................................................................ 106
2.5 BinomialbTheorem ........................................................................... 112
Review ............................................................................................. 116
3 ProbabilitybDistributionsbandbStatistics 118
3.1 RandombVariablesbandbHistograms ................................................... 119
3.2 MeasuresbofbCentralbTendency ......................................................... 131
3.3 MeasuresbofbSpread .......................................................................... 144
3.4 ThebNormalbDistribution .................................................................. 157
3.5 NormalbApproximationbtobthebBinomialbDistribution ....................... 167
3.6 ThebPoissonbDistribution .................................................................. 175
Review ............................................................................................. 183
4 SystemsbofbLinearbEquationsbandbModels 188
4.1 MathematicalbModels ....................................................................... 189
4.2 SystemsbofbLinearbEquations ............................................................ 206
4.3 GaussbEliminationbforbSystemsbofbLinearbEquations ......................... 217
4.4 SystemsbofbLinearbEquationsbWithbNon-UniquebSolutions ............... 236
4.5 MethodbofbLeastbSquares .................................................................. 254
Review ............................................................................................. 266
, 5 Matrices 272
5.1 IntroductionbtobMatrices .................................................................... 273
5.2 MatrixbMultiplication ........................................................................ 283
5.3 InversebofbabSquarebMatrix ................................................................ 300
5.4 AdditionalbMatrixbApplications ........................................................ 312
Review .............................................................................................. 325
M MarkovbChains 328
M.1 MarkovbProcesses ............................................................................. 329
M.2 RegularbMarkovbProcesses ................................................................ 339
M.3 AbsorbingbMarkovbProcesses ............................................................ 345
Review .............................................................................................. 357
G GamebTheory 360
G.1 DecisionbMaking............................................................................... 361
G.2 MixedbStrategybGames ...................................................................... 368
G.3 LinearbProgrammingbandbGamebTheory ............................................ 379
Review .............................................................................................. 388
F Finance 392
F.1 SimplebInterestbandbDiscount ............................................................ 393
F.2 CompoundbInterest............................................................................ 399
F.3 AnnuitiesbandbSinkingbFunds ............................................................ 408
F.4 PresentbValuebofbAnnuitiesbandbAmortization .................................... 416
Review .............................................................................................. 426
AreabUnderbabNormalbCurve 430
AnswersbtobSelectedbExercises 432
Bibliography 447
Index 450
b b
Tomastik/Epstein
,AppliedbFinitebMathematics,bSecondbEdition ©1994,b2008bBrooks/Cole,bCengageb Learning
EdmondbC.bTomastik,bUniversitybofbConnecticut ALLbRIGHTSbRESERVED.bNobpartbofbthisbworkbcoveredbbybthebcopyrightb h
bJanicebL.bEpstein,bTexasbA&MbUniversity ereinbmaybbebreproduced,btransmitted,bstored,borbusedbinbanybformborbbyban
yb meansbgraphic,belectronic,borbmechanical,bincludingbbutbnotblimitedbtobpho
Editor:b CarolynbCrockett
to-
EditorialbAssistant:bRebeccabDashiellb b copying,brecording,bscanning,bdigitizing,btaping,bWebbdistribution,binformatio
MarketingbManager:bMyriahbFitzgibbon nb networks,borbinformationbstoragebandbretrievalbsystems,bexceptbasbpermitt
bTechnicalbEditor:bMarybKanablebIllustr edb underb Sectionb 107b orb 108b ofb theb 1976b Unitedb Statesb Copyrightb Act,b
ator:bJenniferbTribblebPhotographs:bJa withoutb thebpriorbwrittenbpermissionbofbthebpublisher.
nicebEpstein
Forb productb informationb andb technologyb assistance,b contactbusb at
Cengageb Learningb Customerb &b Salesb Support,b 1-800-354-9706.
Forbpermissionbtobusebmaterialbfrombthisbtextborbproduct,bsubmitballb req
uestsbonlinebatbcengage.com/permissions.
Furtherb permissionsb questionsb canb beb e-mailedb to
.
LibrarybofbCongressbControlbNumber:b2008927157
b ISBN-13:b978-0-495-55533-9
ISBN-10:b 0-495-55533-9
Brooks/Cole
10bDavisbDrive
Belmont,bCAb94002-
3098b USA
CengagebLearningbisbableadingbproviderbofbcustomizedblearningbsolutionsbwit
hb officeblocationsbaroundbthebglobe,bincludingbSingapore,bthebUnitedbKingdo
m,b Australia,bMexico,bBrazil,bandbJapan.b Locatebyourblocalbofficebat:bintern
a-b tional.cengage.com/region.
CengagebLearningbproductsbarebrepresentedbinbCanadabbyb Ne
lsonbEducation,bLtd.
Forbyourbcoursebandblearningbsolutions,bvisitbacademic.cengage.com
.b Purchasebanybofbourbproductsbatbyourblocalbcollegebbookstoreborbatb
ourb preferredbonlinebstorebwww.ichapters.com.
PrintedbinbthebUnitedbStatesbofbAmerica
b 1 b2 b3 b4 b5 b6 b7b 12b 11b 10b 09b 08
,Contents
Preface iv
L Logic 2
L.1 IntroductionbtobLogicb .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b . 3
L.2 TruthbTablesb .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b .b . 8
1 SetsbandbProbability 12
1.1 IntroductionbtobSets ............................................................................ 13
1.2 ThebNumberbofbElementsbinbabSet ....................................................... 22
1.3 SamplebSpacesbandbEvents ................................................................. 29
1.4 BasicsbofbProbability........................................................................... 37
1.5 RulesbforbProbability........................................................................... 44
1.6 ConditionalbProbability ...................................................................... 53
1.7 Bayes’bTheorem ................................................................................. 66
Review ............................................................................................... 74
2 CountingbandbProbability 82
2.1 ThebMultiplicationbPrinciplebandbPermutations .................................. 83
2.2 Combinations ..................................................................................... 93
2.3 ProbabilitybApplicationsbofbCountingbPrinciples............................... 100
2.4 BernoullibTrials ................................................................................ 106
2.5 BinomialbTheorem ........................................................................... 112
Review ............................................................................................. 116
3 ProbabilitybDistributionsbandbStatistics 118
3.1 RandombVariablesbandbHistograms ................................................... 119
3.2 MeasuresbofbCentralbTendency ......................................................... 131
3.3 MeasuresbofbSpread .......................................................................... 144
3.4 ThebNormalbDistribution .................................................................. 157
3.5 NormalbApproximationbtobthebBinomialbDistribution ....................... 167
3.6 ThebPoissonbDistribution .................................................................. 175
Review ............................................................................................. 183
4 SystemsbofbLinearbEquationsbandbModels 188
4.1 MathematicalbModels ....................................................................... 189
4.2 SystemsbofbLinearbEquations ............................................................ 206
4.3 GaussbEliminationbforbSystemsbofbLinearbEquations ......................... 217
4.4 SystemsbofbLinearbEquationsbWithbNon-UniquebSolutions ............... 236
4.5 MethodbofbLeastbSquares .................................................................. 254
Review ............................................................................................. 266
, 5 Matrices 272
5.1 IntroductionbtobMatrices .................................................................... 273
5.2 MatrixbMultiplication ........................................................................ 283
5.3 InversebofbabSquarebMatrix ................................................................ 300
5.4 AdditionalbMatrixbApplications ........................................................ 312
Review .............................................................................................. 325
M MarkovbChains 328
M.1 MarkovbProcesses ............................................................................. 329
M.2 RegularbMarkovbProcesses ................................................................ 339
M.3 AbsorbingbMarkovbProcesses ............................................................ 345
Review .............................................................................................. 357
G GamebTheory 360
G.1 DecisionbMaking............................................................................... 361
G.2 MixedbStrategybGames ...................................................................... 368
G.3 LinearbProgrammingbandbGamebTheory ............................................ 379
Review .............................................................................................. 388
F Finance 392
F.1 SimplebInterestbandbDiscount ............................................................ 393
F.2 CompoundbInterest............................................................................ 399
F.3 AnnuitiesbandbSinkingbFunds ............................................................ 408
F.4 PresentbValuebofbAnnuitiesbandbAmortization .................................... 416
Review .............................................................................................. 426
AreabUnderbabNormalbCurve 430
AnswersbtobSelectedbExercises 432
Bibliography 447
Index 450
