ISYE-6644 SIMULATION EXAM NEWEST
ACTUAL EXAM COMPLETE 80
QUESTIONS AND CORRECT DETAILED
ANSWERS (VERIFIED ANSWERS)
|ALREADY GRADED A+||BRAND NEW
VERSION 2026!!!
(8.3)mFindmthemsamplemvariancemofm-3,m-2,m-1,m0,m1,m2,m3m-
mCORRECTmANSWERm14/3m(orm4.666).mIfmsamplemismentirempopulationmthanmvariancemism4.
(8.1)mM/M/1mqueuem-mCORRECTmANSWERmqueuemlengthmhavingmamsinglemserver.
(8.3)mIfmthemexpectedmvaluemofmyourmestimatormequalsmthemparametermthatmyou'remtryingmtomesti
mate,mthenmyourmestimatormismunbiased.mTruemofmFalsem-
mCORRECTmANSWERmTrue.mThismismthemdefinitionmofmunbiasedness
(8.3)mIfmX1,mX2,m...,mXnmaremi.i.d.mwithmmeanmmu,mthenmthemsamplemmeanmX-
barmismunbiasedmformmu.mTruemormFalsem-mCORRECTmANSWERmTrue.
(8.4)mWhatmismthemMSEm(MeanmSquaredmError)mofmanmestimator?m-
mCORRECTmANSWERmBias^2m+mVariance
(8.3)mWhatmismthemexpectedmvaluemofmthemmeanmofmamPois(λ)mrandommvariable?m-
mCORRECTmANSWERmλmismthemmeanmandmthemvariance
(8.3)mWhatmismthemexpectedmsamplemvariancems^2mofmamPois(λ)mrandommvariable?m-
mCORRECTmANSWERmλmismthemsamplemvariancemandmthemmean
, (8.4)mSupposemthatmestimatormAmhasmbiasm=m3mandmvariancem=m12,mwhilemestimatormBmhasmbiasm-
2mandmvariancem=m14.mWhichmestimatorm(AmormB)mhasmthemlowermmeanmsquaredmerror?m-
mCORRECTmANSWERmBmismlower.mBias^2m+mVariance:m18m<m21
MLEm-mCORRECTmANSWERmMaximummLikelihoodmEstimatorm-
m"Ammethodmofmestimatingmthemparametersmofmamdistributionmbymmaximizingmamlikelihoodmfunctio
n,msomthatmundermthemassumedmstatisticalmmodelmthemobservedmdatamismmostmprobable."
(8.4)mSupposemthatmX1=4,mX2=3,mX3=5maremi.i.d.mrealizationsmfrommanmExp(λ)mdistribution.mWhatmi
smthemMLEmofmλ?m-mCORRECTmANSWERm0.25
(8.5/8.6)mIfmX1=2,mX2=−2,mandmX3=0maremi.i.d.mrealizationsmfrommamNor(μm,mσ^2)mdistribution,mwha
tmismthemvaluemofmthemmaximummlikelihoodmestimatemformthemvariancemσ^2?m-
mCORRECTmANSWERm8/3.mMLEmofmσ^2mismthemsummationmofmthemsquaredmdifferencesm(Xim-
mμ),mallmdividedmbymn.
(8.5/8.6)mSupposemwemobservemthemPois(λ)mrealizationsmX1=5,mX2=9mandmX3=1.mWhatmismthemmax
imummlikelihoodmestimatemofmλ?m-
mCORRECTmANSWERm5.mλmismestimatedmasmthemsummationmofmsamplemvaluesmdividedmbymthemnu
mbermofmsamplemvalues.m(5+9+1)/3m=m5
(8.5)mSupposemX1,m...,mXnmaremi.i.d.mBern(p).mFindmthemMLEmformp.m-mCORRECTmANSWERm
(8.7)mSupposemthatmwemhavemamnumbermofmobservationsmfrommamPois(λ)mdistribution,mandmitmturn
smoutmthatmthemMLEmformλmismλhat=5.mWhat'smthemmaximummlikelihoodmestimatemofmPr(X=3)?m-
mCORRECTmANSWERm0.1404.mP(X=x)m=mλ^xm*me^(−λ)m/mx!
(8.6)mTRUEmormFALSE?mIt'smpossiblemtomestimatemtwomMLEsmsimultaneously,me.g.,mformthemNor(μ,σ
2)mdistribution.m-mCORRECTmANSWERmTrue
ACTUAL EXAM COMPLETE 80
QUESTIONS AND CORRECT DETAILED
ANSWERS (VERIFIED ANSWERS)
|ALREADY GRADED A+||BRAND NEW
VERSION 2026!!!
(8.3)mFindmthemsamplemvariancemofm-3,m-2,m-1,m0,m1,m2,m3m-
mCORRECTmANSWERm14/3m(orm4.666).mIfmsamplemismentirempopulationmthanmvariancemism4.
(8.1)mM/M/1mqueuem-mCORRECTmANSWERmqueuemlengthmhavingmamsinglemserver.
(8.3)mIfmthemexpectedmvaluemofmyourmestimatormequalsmthemparametermthatmyou'remtryingmtomesti
mate,mthenmyourmestimatormismunbiased.mTruemofmFalsem-
mCORRECTmANSWERmTrue.mThismismthemdefinitionmofmunbiasedness
(8.3)mIfmX1,mX2,m...,mXnmaremi.i.d.mwithmmeanmmu,mthenmthemsamplemmeanmX-
barmismunbiasedmformmu.mTruemormFalsem-mCORRECTmANSWERmTrue.
(8.4)mWhatmismthemMSEm(MeanmSquaredmError)mofmanmestimator?m-
mCORRECTmANSWERmBias^2m+mVariance
(8.3)mWhatmismthemexpectedmvaluemofmthemmeanmofmamPois(λ)mrandommvariable?m-
mCORRECTmANSWERmλmismthemmeanmandmthemvariance
(8.3)mWhatmismthemexpectedmsamplemvariancems^2mofmamPois(λ)mrandommvariable?m-
mCORRECTmANSWERmλmismthemsamplemvariancemandmthemmean
, (8.4)mSupposemthatmestimatormAmhasmbiasm=m3mandmvariancem=m12,mwhilemestimatormBmhasmbiasm-
2mandmvariancem=m14.mWhichmestimatorm(AmormB)mhasmthemlowermmeanmsquaredmerror?m-
mCORRECTmANSWERmBmismlower.mBias^2m+mVariance:m18m<m21
MLEm-mCORRECTmANSWERmMaximummLikelihoodmEstimatorm-
m"Ammethodmofmestimatingmthemparametersmofmamdistributionmbymmaximizingmamlikelihoodmfunctio
n,msomthatmundermthemassumedmstatisticalmmodelmthemobservedmdatamismmostmprobable."
(8.4)mSupposemthatmX1=4,mX2=3,mX3=5maremi.i.d.mrealizationsmfrommanmExp(λ)mdistribution.mWhatmi
smthemMLEmofmλ?m-mCORRECTmANSWERm0.25
(8.5/8.6)mIfmX1=2,mX2=−2,mandmX3=0maremi.i.d.mrealizationsmfrommamNor(μm,mσ^2)mdistribution,mwha
tmismthemvaluemofmthemmaximummlikelihoodmestimatemformthemvariancemσ^2?m-
mCORRECTmANSWERm8/3.mMLEmofmσ^2mismthemsummationmofmthemsquaredmdifferencesm(Xim-
mμ),mallmdividedmbymn.
(8.5/8.6)mSupposemwemobservemthemPois(λ)mrealizationsmX1=5,mX2=9mandmX3=1.mWhatmismthemmax
imummlikelihoodmestimatemofmλ?m-
mCORRECTmANSWERm5.mλmismestimatedmasmthemsummationmofmsamplemvaluesmdividedmbymthemnu
mbermofmsamplemvalues.m(5+9+1)/3m=m5
(8.5)mSupposemX1,m...,mXnmaremi.i.d.mBern(p).mFindmthemMLEmformp.m-mCORRECTmANSWERm
(8.7)mSupposemthatmwemhavemamnumbermofmobservationsmfrommamPois(λ)mdistribution,mandmitmturn
smoutmthatmthemMLEmformλmismλhat=5.mWhat'smthemmaximummlikelihoodmestimatemofmPr(X=3)?m-
mCORRECTmANSWERm0.1404.mP(X=x)m=mλ^xm*me^(−λ)m/mx!
(8.6)mTRUEmormFALSE?mIt'smpossiblemtomestimatemtwomMLEsmsimultaneously,me.g.,mformthemNor(μ,σ
2)mdistribution.m-mCORRECTmANSWERmTrue
