台灣人工智慧學校(台北)第二期技術領袖培訓班資格考試考古題

台灣人工智慧學校(台北)第二期技術領袖培訓班資格考試考古題. gist僅為備份檔案，rendered題目請見hackmd. 參考解答會在選項前以星號(*)標記，不過目前並不保證一定 ... Skiptocontent Allgists BacktoGitHub Signin Signup Sign in Sign up {{message}} Instantlysharecode,notes,andsnippets. mattwang44/台灣人工智慧學校(台北)第二期技術領袖培訓班資格考試考古題.md LastactiveAug5,2018 Star 0 Fork 0 Star Code Revisions 5 Embed Whatwouldyouliketodo? Embed Embedthisgistinyourwebsite. Share Copysharablelinkforthisgist. Clonevia HTTPS ClonewithGitorcheckoutwithSVNusingtherepository’swebaddress. LearnmoreaboutcloneURLs DownloadZIP Raw 台灣人工智慧學校(台北)第二期技術領袖培訓班資格考試考古題.md 台灣人工智慧學校(台北)第二期技術領袖培訓班資格考試考古題 gist僅為備份檔案，rendered題目請見hackmd 參考解答會在選項前以星號(*)標記，不過目前並不保證一定正確，各位高手可以自行編輯(需登入)提供各題詳解。

感謝提供題目的Anio俊傑和一同討論解題的各位:Sean,MoonyHsieh,johnson,怡中,JackyChang Calculus $f(w,b)=e^{-(2w+b)}$,find$\dfrac{\partialf(w,b)}{\partialw}$at$w=1$,$b=-2$ ($A$)$2$($B$)$1$($C$)$e^{-2}$*($D$)$-2$($E$)$-e^{-1}$ $\dfrac{\partialf(w,b)}{\partialw}=e^{(-2w-b)}(-2)$ $\dfrac{\partialf(1,-2)}{\partialw}=e^{0}(-2)=-2$ Estimatetheextremevalues(localminimumandlocalmaximum)respectively,ofthefunction$f(x)=-2x^3-3x^2+12x$ *($A$)$-20,7$($B$)$0,7$($C$)$-5,20$($D$)$-4,-223$($E$)$-13,5$ $f'(x)=-6x^2-6x+12=-6(x+2)(x-1)$ extremevaluesoccurat$x=-2$or$1$ $f(-2)=-20$,$f(1)=7$ If$f(y)=2y$,where$y(x)=x^3+3x$,find$\dfrac{df}{dx}$at$x=5$. ($A$)$78$($B$)$2$($C$)$0$($D$)$280$*($E$)Noneofabove $\dfrac{\partialf}{\partialx}=\dfrac{\partial}{\partialx}(2x^3+6x)=6x^2+6$ $\dfrac{\partialf(5)}{\partialx}=156$ Suppose$0\leqx\leq1$.Find$x$suchthat$f(x)=-x\log_2x-(1-x)\log_2(1-x)$ismaximized. ($A$)$0$*($B$)$0.5$($C$)$1$($D$)$0.25$($E$)$0.75$ $f'(x)=-\logx-1+\log(1-x)+1=\log(1-x)-\logx$ maximaoccursat$f'(x)=0$,thus$x=0.5$ Afunction$f(x,y)=ax^2+2bxy+cy^2$isbuiltwithrealnumbers$a$,$b$,and$c$.Inwhichconditionsitwillbeguranteedtohaveasaddlepointat$(x,y)=(0,0)$? ($A$)$a>0,ac>b^2$($B$)$a<0,ac>b^2$*($C$)$ac0$($E$)Noneofabove $f(x,y)=ax^2+2bxy+cy^2$ $f_{xx}=2a$,$f_{xy}=f_{yx}=2b$,$f_{yy}=2c$ Hessian$H(x,y)=\begin{bmatrix} 2a&2b\ 2b&2c\ \end{bmatrix}$ criteriaforsaddlepoint:$det(H(x,y))<0$ $ac-b^2<0$ LinearAlgebra Forthematrices$X=\begin{bmatrix} 1&0&-2\ 3&-2&-1\ \end{bmatrix}$and$W=\begin{bmatrix} 1&2\ 9&0\ 1&2\ \end{bmatrix}$,findtheproduct$(XW)$. ($A$)$\begin{bmatrix} 1&-2\ 18&6\ \end{bmatrix}$ *($B$)$\begin{bmatrix} -1&-16\ -2&4\ \end{bmatrix}$ ($C$)$\begin{bmatrix} 7&9&7\ -4&0&-4\ -4&-18&-4\ \end{bmatrix}$ ($D$)$\begin{bmatrix} 7&-4&-4\ 9&0&-18\ 7&-4&-4\ \end{bmatrix}$ ($E$)Noneofabove $(XW)^T=W^TX^T=\begin{bmatrix} -1&-16\ -2&4\ \end{bmatrix}$ Aneigenvalueofmatrix$A$isascalar$\lambda$suchthat$det(\lambdaI-A)=0$.Findtheeigenvaluesforthematrix$A=\begin{bmatrix} 1&2&1\ 6&-1&0\ -1&-2&-1\ \end{bmatrix}$ ($A$)$\lambda=-3,0,2$ ($B$)$\lambda=3,1,4$ ($C$)$\lambda=-2,0,1$ *($D$)$\lambda=3,0,-4$ ($E$)$\lambda=-4,-1,2$ $det(A-\lambdaI)=-\lambda^3-\lambda^2+12\lambda=\lambda(\lambda-3)(\lambda+4)$ $\lambda=0,3,-4$ For$AX=B$,where$A=\begin{bmatrix} 1&2\ 2&-1\ \end{bmatrix}$and$B=\begin{bmatrix} -1&1\ -12&7\ \end{bmatrix}$,find$X^{-1}$. *($A$)$\begin{bmatrix} 1&3\ 2&5\ \end{bmatrix}$($B$)$\begin{bmatrix} -25&15\ 10&-5\ \end{bmatrix}$($C$)$\begin{bmatrix} -1&-2\ -2&1\ \end{bmatrix}$($D$)$\begin{bmatrix} -5&-3\ -2&-1\ \end{bmatrix}$($E$)$\begin{bmatrix} 7&-1\ 12&1\ \end{bmatrix}$ $X^{-1}=B^{-1}A=\begin{bmatrix} 1&3\ 2&5\ \end{bmatrix}$ Giventwovectors$\vec{u}=(1,0,-2)$and$\vec{v}=(2,1.5,1)$,findthe$L^2$norm(Euclideandistance)$\vec{v}-\vec{u}$andtheanglebetweenthem. ($A$)distance=$1$,angle=$30^{\circ}$ ($B$)distance=$1.5$,angle=$60^{\circ}$ ($C$)distance=$2$,angle=$75^{\circ}$ ($D$)distance=$2.5$,angle=$45^{\circ}$ *($E$)distance=$3.5$,angle=$90^{\circ}$ $d=\sqrt{(2-1)^2+(1.5-0)^2+(1-(-2))^2}=3.5$ $\theta=\cos^{-1}(\dfrac{u\cdotv}{\vertu\vert\vertv\vert})=\cos^{-1}(0)=\dfrac{\pi}{2}$ Forwhichvaluesof$a$aretherenosolutions,manysolutions,orauniquesolutiontothesystemgivenbelow? $x+y=1$ $6x+6y=a$ ($A$)$a=6$,$a\neq6$,none ($B$)$a\neq6$,none,$a=6$ *($C$)$a\neq6$,$a=6$,none ($D$)$a=6$,none,$a\neq6$ ($E$)none,$a\neq6$,$a=6$ $x+y=a/6$ nosolution:$a/6\neq1$ infinitesolutions:$a/6=1$ nosolution:none Statistics&Probability Given$P(A)=0.25$,$P(B)=0.5$,$P(A\vertB)=0.1$,whatis$P(B\vertA)$? ($A$)$0.16$*($B$)$0.2$($C$)$0.55$($D$)$0.65$($E$)$0.74$ $0.1*0.5/0.25=0.2$ Assumethat$P(A)=0.4$and$P(B)=0.3$.If$A$and$B$aremutuallyexclusive,whatis$P(A$or$B)$? *($A$)$0.7$($B$)$0.58$($C$)$0.88$($D$)$0.1$($E$)Noneofabove $0.3+0.4=0.7$ Supposearandomexperimenthasthefollowingcharacteristics. (1)Thereare$n$identicalandindependenttrialsofacommonprocedure. (2)Thereareexactlytwopossibleoutcomesforeachtrial,onetermed"success"andtheother"failure." (3)Theprobabilityofsuccessonanyonetrialisthesamenumber$q$. Wealsosaythat$X$hasabinomialdistributionwithparameters$n$and$q$.Asweknow,$Var(X)=nq(1-q)$.Find$E(X^2)$. Hint:$E(X^2)=E(X-\mu+\mu)^2=E(X-\mu)^2-2E[(X-\mu)\mu]+E(\mu^2)=...$ ($A$)$nq^2+nq(n+1)$ *($B$)$nq+nq^2(n-1)$ ($C$)$nq-nq^2(n-1)$ ($D$)$nq+nq^2(n-1)$ ($E$)$nq^2-nq(n-1)$ Supposeyou'reonagameshow,andyou'regiventhechoiceofthreedoors:Behindonedoorisacar;behindtheothers,goats.Youpickadoor,sayNo.1,andthehost,whoknowswhat'sbehindthedoors,opensanotherdoor,sayNo.3,whichhasagoat.Hethensaystoyou,"DoyouwanttopickdoorNo.2?"Isittoyouradvantagetoswitchyourchoice? *($A$)Yes($B$)No($C$)Switchingornotwillnotchangethewinningprobability. PleaseseetheintroductionofMontyHallproblemorthisChinesepostwithillustrativeexample. Whichofthefollowingstatementsaretrue? I.Allvariablescanbeclassifiedasquantitativeorcategoricalvariables. II.Categoricalvariablescanbecontinuousvariables. III.Quantitativevariablescanbediscretevariables. ($A$)Ionly($B$)IIonly($C$)IIIonly($D$)IandII*($E$)IandIII Accordingtothechart,whichofthefollowingstatementsaretrue? 16.Thedotplotbelowshowsthenumberoftelevisionsownedbyeachfamilyonacityblock. *($A$)Thedistributionisright-skewedwithnooutlier. ($B$)Thedistributionisright-skewedwithmanyoutliers. ($C$)Thedistributionisleft-skewedwithnooutliers. ($D$)Thedistributionisleft-skewedwithmanyoutliers. ($E$)Thedistributionissymmetric. Anationalachievementtestisadministeredannuallyto3rdgraders.Thetesthasameanscoreof80andastandarddeviationof15.IfJane'sz-scoreis$-1.20$,whatwasherscoreonthetest? *($A$)62($B$)68($C$)85($D$)92($E$)98 $z=\dfrac{x-\mu}{\sigma}$,$-1.2=\dfrac{x-80}{15}$ $x=62$ Whenwearefittingtheregressionmodel,weusuallyusesumofthesquarederrortoevaluateourregressionmodel.Thisnumbermeasuresthegoodnessoffitofthelinetothedata.Inthiscase,aregressionmodelhasalowersumofthesquarederrorandit'sbettermodelforourdataset. Data1 Data2 Data3 Data4 Data5 x 2 2 6 8 0 y 0 1 2 3 3 Whichofthemodelsshownbelowisthebestone,havingaminimalsquarederror? ($A$)$\hat{y}=0.35x-0.125$ ($B$)$\hat{y}=-0.35x+0.125$ ($C$)$\hat{y}=0.65x-0.45$ ($D$)$\hat{y}=-0.6x-0.125$ *($E$)$\hat{y}=0.35x+0.55$ Squarederrorof5models: 10.383125,59.083125,17.8125,112.508125,8.1725 Whichofthefollowingstatementsaretrue? I.Whenthesumoftheresidualsisgreaterthanzero,thedatasetisnonlinear. II.Arandompatternofresidualssupportsalinearmodel. III.Arandompatternofresidualssupportsanonlinearmodel. ($A$)Ionly*($B$)IIonly($C$)IIIonly($D$)IandII($E$)IandIII Therandomvariable$Z$isnormallydistributed.Meanof$Z$is$430$,andthevalue$Z=300$isthe14thpercentileofthedistribution.Whichisthebestestimateofthestandarddeviationofthedistribution. *($A$)125($B$)135($C$)145($D$)155($E$)165 Programming Createacustomfunction,Derivative(),whichcancomputethefirstderivativeofagivenfunction$f(x)$withrespectto$x$viaCentralDifferenceMethod,definedas$\lim_{h\to0}\dfrac{f(x+\dfrac{h}{2})-f(x-\dfrac{h}{2})}{h}$. NOTE:Supposetheonlyavailablefunctionisprint()andletusset$h=1.0e-1$. #python參考程式碼 defderivative(f,x,h,order): iforder==0: returnf(x) else: return(derivative(f,x+h/2,h,order-1)-derivative(f,x-h/2,h,order-1))/h ATaylorseriesofafunction$g(x)$around$x=a$isdefinedbythefollowingseriesexpansion,$\sum_{n=0}^\infty\dfrac{g^{(n)}(a)}{n!}(x-a)^n$,where$g^{(n)}$denotes$n^{\text{th}}$derivativeof$g(x)$.Now,given$g(x)=2^x+2x^7$,trytocreateacustomfunction,Taylor_Expansion(),tocompute$g(x=3)$byusingTaylorseries($a=0$)upto$7^{\text{th}}$orderin$n$.Youshouldfindthatwhiletheanswerdeviatesfromtheexactsolution$g(x=3)$obtainedfromadirectsubstitution,theerrorislessthan$3%$. HINT:Youcantake$x=3,a=0$andkeepthesummationonlyupto$n=7$intheseiesformula. NOTE:Theonlyavailablefunctionisprint()andthecustomfunctionyougotin$1.$isuseful. defderivative(f,x,h,order): iforder==0: returnf(x) else: return(derivative(f,x+h/2,h,order-1)-derivative(f,x-h/2,h,order-1))/h deffactorial(n): if(n<=1): return1 else: returnfactorial(n-1)*n defTaylor_Expansion(f,x,a,h,order): ans=0 foriinrange(order+1): ans+=derivative(f,a,h,i)*((x-a)**i)/factorial(i) returnans defg(x): return2**x+2*x**7 h=0.1 x=3 a=0 order=7 A=g(x) T=Taylor_Expansion(g,x,a,h,order) print(A)#4382 print(T)#4424.5478396 Signupforfree tojointhisconversationonGitHub. Alreadyhaveanaccount? Signintocomment Youcan’tperformthatactionatthistime. Yousignedinwithanothertaborwindow.Reloadtorefreshyoursession. Yousignedoutinanothertaborwindow.Reloadtorefreshyoursession.