台灣人工智慧學校新竹分校第一期技術領袖培訓班資格考試考古題

2024-11-22

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台灣人工智慧學校新竹分校第一期技術領袖培訓班資格考試考古題. gist僅為備份用檔案，完整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 ... Skiptocontent Allgists BacktoGitHub Signin Signup Sign in Sign up {{message}} Instantlysharecode,notes,andsnippets. mattwang44/台灣人工智慧學校新竹分校第一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 3 Embed Whatwouldyouliketodo? Embed Embedthisgistinyourwebsite. Share Copysharablelinkforthisgist. Clonevia HTTPS ClonewithGitorcheckoutwithSVNusingtherepository’swebaddress. LearnmoreaboutcloneURLs DownloadZIP Raw 台灣人工智慧學校新竹分校第一期技術領袖培訓班資格考試考古題.md 台灣人工智慧學校新竹分校第一期技術領袖培訓班資格考試考古題 gist僅為備份用檔案，完整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)更正答案或提供各題詳解。

感謝一同討論解題的各位:Paul,陳彥吉,游聲峰Robert,Sean,MoonyHsieh,johnson,怡中 Calculus Letthefunction$f(x)=ax^3+bx^2+cx+d$.Supposethat$f(0)=4$isacriticalpointof$f$and$f(1)=-2$isapointofinflection,find$a$,$b$,$c$and$d$. Hint:Thecriticalpointof$f$isthepointsuchthat$f'(x)=0$,andthepointofinflectionof$f$satify$f''(x)=0$. ($A$)$a=1$,$b=5$,$c=8$,$d=6$ ($B$)$a=13$,$b=-3$,$c=-5$,$d=4$ *($C$)$a=3$,$b=-9$,$c=0$,$d=4$ ($D$)$a=6$,$b=11$,$c=1$,$d=-2$ $f(x)=ax^3+bx^2+cx+d$ $f'(x)=3ax^2+2bx+c$ $f''(x)=6ax+2b$ Thensolve: $f(0)=d=4$...(1) $f(1)=a+b+c+d=-2$...(2) $f'(0)=c=0$...(3) $f''(1)=6a+2b=0$...(4) Findthe$(x,y)\in{(x,y)|2x^2-y^2=1}$whichminimizesthedistancefrom$(3,0)$,andwhatistheminimaldistance$d$? ($A$)$(x,y)=(3,\pm4)$,$d=2$ ($B$)$(x,y)=(8,17)$,$d=23$ ($C$)$(x,y)=(3,0)$,$d=\sqrt{3}$ *($D$)$(x,y)=(3,\pm1)$,$d=\sqrt{5}$ Thepointsgivenin(A)(B)(C)doesn'tmeettheequation. Findtheequationofthetangentlineto$y=2^x$at$(1,2)$ *($A$)$y=x\ln{4}-\ln{4}+2$ ($B$)$y=8x\exp^x-4x+3$ ($C$)$y=-\sqrt[3]{x}+1$ ($D$)$y=\ln{6^x}+9x$ Onlytheequationlistedin(A)isalinearequation Let$f(x,y)=sin(x^2-y)$,find$\dfrac{\partial^2f(2,4)}{\partialx\partialy}$ ($A$)5($B$)9($C$)4*($D$)0 $\dfrac{\partial^2f(2,4)}{\partialx\partialy}=\sin(x^2-y)*2x=0$ Let$z=f(x-y,y-x)$,whatis$\dfrac{\partialz}{\partialx}+\dfrac{\partialz}{\partialy}$? ($A$)1*($B$)0($C$)6($D$)2 Alwaysresultsinpairsofpostiveandnegativetermsthathavesamevalues. LinearAlgebra Let$A=\begin{bmatrix} 1&2&1\ 0&1&2\ 1&3&2 \end{bmatrix}$,findamatrix$B$suchthat$AB=A^2+2A$ ($A$)$\begin{bmatrix} 3&2&1\ 0&7&2\ 1&1&6 \end{bmatrix}$*($B$)$\begin{bmatrix} 3&2&1\ 0&3&2\ 1&3&4 \end{bmatrix}$($C$)$\begin{bmatrix} 3&7&8\ 3&3&7\ 13&5&4 \end{bmatrix}$($D$)$\begin{bmatrix} 9&2&1\ 7&2&4\ 6&3&6 \end{bmatrix}$ $B=A^{-1}(A^2+2A)=A+2I$ where$I$denotestheidentitymatrix. Whatistherankof$\begin{bmatrix} 1&2&3&4&5\ 1&0&0&1&0\ 1&1&1&1&1\ 2&2&3&5&5\ 5&5&7&11&11\ \end{bmatrix}$? ($A$)5($B$)6($C$)2*($D$)3 Pleasecheckoutthedefinitionofrank Findtheeigenvaluesofthefollowingmatrix$\begin{bmatrix} 1&1&2&2\ 1&1&2&2\ 2&2&1&1\ 2&2&1&1\ \end{bmatrix}$? Hint:TryGaussianeliminationfirst. ($A$)0,1,-6($B$)3,5,-10*($C$)0,6,-2($D$)0,6,12 Findthesolutionsetforthefollowinglinearmatrixequation $Ax=\begin{bmatrix} 1&0&1&0\ 2&2&0&3\ 0&4&-4&5\ \end{bmatrix}\begin{bmatrix} x_1\x_2\x_3\x_4\ \end{bmatrix}=\begin{bmatrix} 2\1\7 \end{bmatrix}$ *($A$)$\begin{Bmatrix}\left. \begin{bmatrix} -t+2\t-3\t\1\ \end{bmatrix}\right\rvertt\inF \end{Bmatrix}$($B$)$\begin{Bmatrix}\left. \begin{bmatrix} t+2\10t\t\3t+1\ \end{bmatrix}\right\rvertt\inF \end{Bmatrix}$($C$)$\begin{Bmatrix}\left. \begin{bmatrix} t\3t\-t-10\1\ \end{bmatrix}\right\rvertt\inF \end{Bmatrix}$ ($D$)$\begin{Bmatrix}\left. \begin{bmatrix} 3t\t\t+10\5\ \end{bmatrix}\right\rvertt\inF \end{Bmatrix}$ Forwhich$x$is$A=LU$decomposiitionimpossible? $A=\begin{bmatrix} 1&2&0\ 3&x&1\ 0&1&1\ \end{bmatrix}$ *($A$)$x=6$($B$)$x=4$($C$)$x=12$($D$)$x=0$ If$A$isinvertible,thenitadmitsanLUfactorizationifandonlyifallitsleadingprincipalminorsarenonzero. Statistics&Probability Whichofthefollowingstatementsaretrue? I.Qualitativevariablescouldbemultiplied. II.Categoricalvariablescouldbecontinuousvariables. III.Quantitativevariablescouldbediscretevariables. ($A$)Ionly($B$)IIonly($C$)IIIonly($D$)IandII*($E$)IandIII Assumethat$P(A)=0.4$and$P(B)=0.3$,and$P(A$or$B)=0.7$,$P(A)*P(B)=0.12$.Whichoffollowingstatementsaretrue? I.$A$and$B$aremutuallyexclusive II.$P(A$and$B)=0.7$ III.$A$and$B$areindependentevent ($A$)Ionly($B$)IIonly($C$)IIIonly($D$)IandII*($E$)IandIII Avariablefollownormaldistribution.Ithasameanvalueof$80$andastandarddeviationof$15$.Ifaz-scoreis$2$,what'svalueonthenormaldistribution? ($A$)68($B$)95($C$)99*($D$)110($E$)125 Adistributionthatskewnessvalueabove$2.5$($SK>2.5$),whicchoffollowingstatementsaretrue? *($A$)mean>median>mode ($B$)mode>mean>median ($C$)mode>median>mean ($D$)mean=median=mode ($E$)noneabove Assuming$P(A1)=0.3$,$P(A2)=0.7$,$P(B\vertA1)=0.2$,and$P(B\vertA2)=0.4$,${A1,A2}$isapartitionof$U$,then$P(A1\vertB)$? ($A$)0.111*($B$)0.177($C$)0.272($D$)0.323($E$)0.37 Assumethat$X$isarandomvariableandits$E(X)=100$and$\sigma^2(X)=10$.Thevariable$Y$isalinearfunctionof$X$,$Y=2X+50$.That$E(Y)$and$\sigma^2(Y)$,whichoffollowingstatementsaretrue? I.$E(Y)=100$ II.$E(Y)=200$ III.$\sigma^2(Y)=10$ IV.$\sigma^2(Y)=40$ ($A$)Ionly($B$)IIonly($C$)IIIonly*($D$)IVonly($E$)noneabove Ineachcasestatewhetheryouexpectthetwovariables$x$and$y$indicatedtohavepositive,negative,orzerocorrelation.Whichoffollowingstatementsisnegative? ($A$)Thenumber$x$ofpafesinabookandtheage$y$oftheauthor. ($B$)Thenumber$x$ofpafesinabookandtheage$y$oftheintendedreader. *($C$)Theweight$x$ofanautomobileandthefueleconomy$y$inmilespergallon. ($D$)Theweight$x$ofanautomobileandthereading$y$onitsodometer. ($E$)Theamount$x$ofasedativeapersontookanhouragoandthetime$y$ittakeshimtorespondtoastimulus. Asthefigure,whichoffollowingstaementsaretrue? ($A$)SetI.SSE0$ ($D$)$y=\beta_1x+\beta_2$,SetI.$r^2<0$andSetII.$r^2=0$ ($E$)noneabove. Asampleofsize$n=150$hasmean$x=30$andstandarddeviation$s=3$.Withoutknowinganythingelseaboutthesample,whatcanbesaidaboutthenumberofobservationsthatlieintheinterval$(24,36)$ *($A$)Atleast75% ($B$)Atleast85% ($C$)Atleast90% ($D$)Atleast95% ($E$)noneabove $s^2=\frac{n(1-p)*(2s)^2}{n}$ $1=(1-p)*4$ $p=75%$ Whichfollowingtableisavalidprobabilitydistributionofadiscreterandomvariable? ($A$) x -2 0 2 4 6 P(x) 0.2 0.5 0.2 0.1 0.1 ($B$) x 0 1 2 3 4 --- --- --- --- --- --- P(x) 0.2 0.2 0.2 0.1 0.1 ($C$) x 0.5 0.25 0.3 0.4 0.7 --- --- --- --- --- --- P(x) 0.2 -0.3 0.2 -0.1 0.1 *($D$) x -1 0 1 3 5 --- --- --- --- --- --- P(x) 0.2 0.3 0.2 0.2 0.1 ($E$)noneabove Programming 本部份共有兩大題(合計三小題)，每題依序為6分,8分,6,分,合計20分。

程式題請使用偽代碼(pseudocode)作答。

PseudocodeisasimplewayofwritingprogrammingcodeinEnglish.Pseudocodeisnotactualprogramminglanguage.Itusesshortphrasestowritecodeforprogramsbeforeyouactuallycreateitinaspecificlanguage.Thepurposeofusingpseudocodeisthatitiseasierforpeopletounderstandthelogicbehindthealgorithms. ・Rulesforpseudocode,Writeonlyonestatementperline ・Availablekeywords:IF,ELSE,ENDIF,WHILE,ENDWHILE,REPEAT,UNTIL,FUNCTION,FOR,PRINT,LENGTH example1: functionexample1(x){ ydata[j+1]) func1(data,j,j+1); } } } 參考解答:[1,1,5,6,8,9,13,22] PleasecheckBubblesort. (2)Defineafunctionwhichsatisfiesthefollowingstaement. Given${x_n}$,alistofunsortednumbers,returnthesumofthefirstquartile$Q1$andthethirdquartile$Q3$. Hints: $$Q_x= \left{ \begin{array}{l} a_{z+1}&\text{if}z+1>\dfrac{nx}{4}>z\ \dfrac{a_{z}+a_{z+1}}{2}&\text{if}\dfrac{nx}{4}=z \end{array} \right. $$ $z$isaninteger $n$isthelengthofgivenlistofnumbers ${a_n}$isthesortedlistof${x_n}$ 參考解答: functionswap(x,i,j){ vara; adata[j+1]) func1(data,j,j+1); } } } functionfunc(data){ varlen=length(data); varx[len]=sort(data); varq1,q3; if(len%4==0){ q1=(x[len/4-1]+x[len/4])/2; q3=(x[(len*3)/4-1]+x[(len*3)%4])/2; } else{ q1=x[len/4]; q3=x[(len*3)/4]; } returnq1+q3; } Signupforfree tojointhisconversationonGitHub. Alreadyhaveanaccount? Signintocomment Youcan’tperformthatactionatthistime. Yousignedinwithanothertaborwindow.Reloadtorefreshyoursession. Yousignedoutinanothertaborwindow.Reloadtorefreshyoursession.