Instructor Solution Manual
f f
Probability and Statistics for Engineers and Scientists(3
f f f f f f f
rd Edition)
f
AnthonyfHayter
, 1
InstructorfSolutionfManual
Thisfinstructorfsolutionfmanualftofaccompanyfthefthirdfeditionfof
“ProbabilityfandfStatisticsfforfEngineersfandfScientists”fbyfAnthonyfHayter
providesfworkedfsolutionsfandfanswersftofallfoffthefproblemsfgivenfinftheftextbook.fThefstudentfsoluti
onfmanualfprovidesfworkedfsolutionsfandfanswersftofonlyfthefodd-
numberedfproblemsfgivenfatfthefendfoffthefchapterfsections.fInfadditionftofthefmaterialfcontaine
dfinfthefstudentfsolutionfmanual,fthisfinstructorfmanualfthereforefprovidesfworkedfsolutionsfan
dfanswersftofthefeven-
numberedfproblemsfgivenfatfthefendfoffthefchapterfsectionsftogetherfwithfallfoffthefsupplement
aryfproblemsfatfthefendfoffeachfchapter.
,2
, Contents
1 Probabilityf Theory 7
1.1 Probabilities ......................................................................................................................... 7
1.2 Events.................................................................................................................................... 9
1.3 Combinationsf off Events ................................................................................................... 13
1.4 Conditionalf Probability.................................................................................................... 16
1.5 Probabilitiesf off Eventf Intersections .............................................................................. 22
1.6 Posteriorf Probabilities ..................................................................................................... 28
1.7 Countingf Techniques........................................................................................................ 32
1.9 Supplementaryf Problems ................................................................................................ 37
2 Randomf Variables 49
2.1 Discretef Randomf Variables ............................................................................................. 49
2.2 Continuousf Randomf Variables ....................................................................................... 54
2.3 Thef Expectationf off af Randomf Variable ......................................................................... 58
2.4 Thef Variancef off af Randomf Variable .............................................................................. 62
2.5 JointlyfDistributedf Randomf Variables ......................................................................... 68
2.6 CombinationsfandfFunctionsfoffRandomfvariables..................................................... 77
2.8 Supplementaryf Problems ................................................................................................ 86
3 Discretef Probabilityf Distributions 95
3.1 Thef Binomialf Distribution .............................................................................................. 95
3.2 ThefGeometricfandfNegativefBinomialfDistributions ................................................ 99
3.3 Thef HypergeometricfDistribution ................................................................................ 102
3.4 Thef PoissonfDistribution ............................................................................................... 105
3.5 Thef MultinomialfDistribution ...................................................................................... 107
3.7 Supplementaryf Problems .............................................................................................. 109
4 Continuousf Probabilityf Distributions 113
4.1 Thef Uniformf Distribution.............................................................................................. 113
4.2 Thef ExponentialfDistribution ....................................................................................... 116
4.3 Thef Gammaf Distribution............................................................................................... 119
4.4 Thef Weibullf Distribution ............................................................................................... 121
4.5 Thef Betaf Distribution..................................................................................................... 123
4.7 Supplementaryf Problems .............................................................................................. 125
3
f f
Probability and Statistics for Engineers and Scientists(3
f f f f f f f
rd Edition)
f
AnthonyfHayter
, 1
InstructorfSolutionfManual
Thisfinstructorfsolutionfmanualftofaccompanyfthefthirdfeditionfof
“ProbabilityfandfStatisticsfforfEngineersfandfScientists”fbyfAnthonyfHayter
providesfworkedfsolutionsfandfanswersftofallfoffthefproblemsfgivenfinftheftextbook.fThefstudentfsoluti
onfmanualfprovidesfworkedfsolutionsfandfanswersftofonlyfthefodd-
numberedfproblemsfgivenfatfthefendfoffthefchapterfsections.fInfadditionftofthefmaterialfcontaine
dfinfthefstudentfsolutionfmanual,fthisfinstructorfmanualfthereforefprovidesfworkedfsolutionsfan
dfanswersftofthefeven-
numberedfproblemsfgivenfatfthefendfoffthefchapterfsectionsftogetherfwithfallfoffthefsupplement
aryfproblemsfatfthefendfoffeachfchapter.
,2
, Contents
1 Probabilityf Theory 7
1.1 Probabilities ......................................................................................................................... 7
1.2 Events.................................................................................................................................... 9
1.3 Combinationsf off Events ................................................................................................... 13
1.4 Conditionalf Probability.................................................................................................... 16
1.5 Probabilitiesf off Eventf Intersections .............................................................................. 22
1.6 Posteriorf Probabilities ..................................................................................................... 28
1.7 Countingf Techniques........................................................................................................ 32
1.9 Supplementaryf Problems ................................................................................................ 37
2 Randomf Variables 49
2.1 Discretef Randomf Variables ............................................................................................. 49
2.2 Continuousf Randomf Variables ....................................................................................... 54
2.3 Thef Expectationf off af Randomf Variable ......................................................................... 58
2.4 Thef Variancef off af Randomf Variable .............................................................................. 62
2.5 JointlyfDistributedf Randomf Variables ......................................................................... 68
2.6 CombinationsfandfFunctionsfoffRandomfvariables..................................................... 77
2.8 Supplementaryf Problems ................................................................................................ 86
3 Discretef Probabilityf Distributions 95
3.1 Thef Binomialf Distribution .............................................................................................. 95
3.2 ThefGeometricfandfNegativefBinomialfDistributions ................................................ 99
3.3 Thef HypergeometricfDistribution ................................................................................ 102
3.4 Thef PoissonfDistribution ............................................................................................... 105
3.5 Thef MultinomialfDistribution ...................................................................................... 107
3.7 Supplementaryf Problems .............................................................................................. 109
4 Continuousf Probabilityf Distributions 113
4.1 Thef Uniformf Distribution.............................................................................................. 113
4.2 Thef ExponentialfDistribution ....................................................................................... 116
4.3 Thef Gammaf Distribution............................................................................................... 119
4.4 Thef Weibullf Distribution ............................................................................................... 121
4.5 Thef Betaf Distribution..................................................................................................... 123
4.7 Supplementaryf Problems .............................................................................................. 125
3
