Review for the Midterm Exam.
|
|
- Florence McDowell
- 6 years ago
- Views:
Transcription
1 Review for he iderm Exm Rememer! Gross re e re Vriles suh s,, /, p / p, r, d R re gross res 2 You should kow he disiio ewee he fesile se d he udge se, d kow how o derive hem The Fesile Se Wihou goverme purhses:, 2,, 2, g Wih goverme purhses : The golde rule lloio is deermied he poi of ge ewee he fesile se lie d idifferee urve he slope of oh lies re he sme The Budge Se Firs period udge osri:, m Seod period udge osri: 2, m Lifeime udge osri:, 2, These equios re he si seup The m ler uder differe ssumpios, suh s whe xes, rsfers d pils re preseed The moer equilirium lloio is deermied he poi of ge ewee he lifeime udge se lie d idifferee urve he slope of udge se lie equls he slope of idifferee urve 3 You fid he vlue of fi moe solvig moe-mrke lerig odiio oe-rke Clerig Codiio Suppl of fi moe: Demd for fi moe:, Re of Reur o Fi oe The re of reur o fi moe ells ou how m goods ou oi i he fuure if oe ui of he good is sold for moe od
2 ,, Prie level Prie is os of eh good: / p Iflio: / p p 4 You should kow he osequees of iresig sok of fi moe oe reio e irodued io he eoom mes of susidies or seigiorge You should e le o expli i whih ses he moer equiliri i he golde rule, d i whih ses he do o The moe suppl expsio: Goverme udge osri wih susidies o old people: Goverme udge osri wih seigiorge: G 5 You should udersd he differee mog ieriol moer rrgemes Wh does i me foreig urre orols, ooperive siliio d uilerl defese of he exhge re? Foreig Curre Corols The vlue of fi moe is idepedel deermied eh our s moe demd d suppl, Exhge re wih foreig urre orols: e
3 Wihou Foreig Curre Corols People re free o hold d use he moe of our We o loger deermie he moe suppl d demd of eh our seprel The world moe-mrke lerig odiio: e,, The exhge re o e deermied i his se Cooperive siliio is he firs soluio o he ideermi of he exhge re Boh ouries gree o work ogeher priig more moe i order o keep he exhge re fixed Uilerl defese is he seod soluio Foreig our will o oopere I order o mii he fixed exhge re, ol domesi our will hoor is pledge o exhge urre xig is ow iie 6 Wih he presee of lerive sses, i order o eourge people o hold sse simuleousl, he re of reur o ever sse mus e ideil We refer o his proper s re-of-reur equli ; ll sses re perfe susiues 7 I he se of imperfe susiues, oher sses ield he higher reur h moe We ssume h people sill hold moe euse i is more liquid 8 You should kow he defiiio of liquidi; wh moe is more liquid h oher sses? You lso should e le o derive he udge osri uder hree-period lived model Firs period udge osri:, m k Seod period udge osri: 2, m Third period udge osri: 3, 2 Xk Lifeime udge osri:, 2, 3, 2 X X is wo-period re of reur o pil, while x X is oe-period re of reur o pil Tol oupu: GDP X k Whe sses ield rdom re of reur, we would expe re-of-reur equli o hold o verge The expeed re of reur is mesured he
4 summio of ll possile res of reur muliplied heir respeive proiliies E r π r π 2r2 π r 0 You should e le o expli he differee ewee he omil ieres re R omil re of reur o lo d he rel ieres re r rel re of reur o lo p R r p You should kow wh we eed o hve fiil iermediios d erl ks How ks mke profis? Wh does i me fiil iermediries? Wh re odiios d ke eoomi vriles oe reserve requiremes d erl k ledig irodued? 2 ke sure h ou kow he defiiio of differe mesures of moe; 0,, 2d 3 0 iludes ol urre; i is ol fi moe sok i our model is lled he ol moe sok; i iludes 0 plus highl liquid sses Wh is he relio ewee d? 3 Uder ompeiive mrke, here exis m ks i he eoom These ks will ompee offerig people higher ieres re o deposis The ieres re will fill equls o he reur o sses ks hve Wihou Reserve Requiremes Rel re of reur o deposis or rel ieres re: r * x X Wih Reserve Requiremes oe-mrke lerig odiio: γ h oe h ow reserve requiremes represe he ol demd for fi moe euse people o loger hold fi moe Prie level: p γ h Rel ieres re: r* γ γ X oe h ow ks hold wo pes of sses; reserved fi moe d pil Tol oupu: GDP Xk X γ h
5 oe h Xk 2 is he oupu produed pils people ivesed wo periods go X γ h 2 is he oupu produed pils ks ivesed wo periods go γ h is he mou ks ives from deposis fer sisfig he reserve requiremes Wih Cerl Bk Ledig Bks ow hve wo soures o quire reserve requiremes: o o-orrowed pr: o Borrowed pr: δγ h, where δ is he frio of k s reserves fied los from he erl k ψ is he re hrged he erl k oe-mrke lerig odiio: γ h δγ h Prie level: p γ δ h Rel ieres re: r * γ [ γ δ ] X ψδγ Tol oupu: GDP Xk X [ γ δ ] h
Week 8 Lecture 3: Problems 49, 50 Fourier analysis Courseware pp (don t look at French very confusing look in the Courseware instead)
Week 8 Lecure 3: Problems 49, 5 Fourier lysis Coursewre pp 6-7 (do look Frech very cofusig look i he Coursewre ised) Fourier lysis ivolves ddig wves d heir hrmoics, so i would hve urlly followed fer he
More informationSuggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c)
per I. Le α 7 d β 7. The α d β re he roos o he equio, such h α α, β β, --- α β d αβ. For, α β For, α β α β αβ 66 The seme is rue or,. ssume Cosider, α β d α β y deiiio α α α α β or some posiive ieer.
More informationDERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR
Bllei UASVM, Horilre 65(/008 pissn 1843-554; eissn 1843-5394 DERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR Crii C. MERCE Uiveriy of Agrilrl iee d Veeriry Mediie Clj-Npo,
More informationF.Y. Diploma : Sem. II [CE/CR/CS] Applied Mathematics
F.Y. Diplom : Sem. II [CE/CR/CS] Applied Mhemics Prelim Quesio Pper Soluio Q. Aemp y FIVE of he followig : [0] Q. () Defie Eve d odd fucios. [] As.: A fucio f() is sid o e eve fucio if f() f() A fucio
More informationDIFFERENCE EQUATIONS
DIFFERECE EQUATIOS Lier Cos-Coeffiie Differee Eqios Differee Eqios I disree-ime ssems, esseil feres of ip d op sigls pper ol speifi iss of ime, d he m o e defied ewee disree ime seps or he m e os. These
More informationPhysics 232 Exam I Feb. 13, 2006
Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.
More informationLOCUS 1. Definite Integration CONCEPT NOTES. 01. Basic Properties. 02. More Properties. 03. Integration as Limit of a Sum
LOCUS Defiie egrio CONCEPT NOTES. Bsic Properies. More Properies. egrio s Limi of Sum LOCUS Defiie egrio As eplied i he chper iled egrio Bsics, he fudmel heorem of clculus ells us h o evlue he re uder
More informationMath 2414 Homework Set 7 Solutions 10 Points
Mah Homework Se 7 Soluios 0 Pois #. ( ps) Firs verify ha we ca use he iegral es. The erms are clearly posiive (he epoeial is always posiive ad + is posiive if >, which i is i his case). For decreasig we
More informationReinforcement Learning
Reiforceme Corol lerig Corol polices h choose opiml cios Q lerig Covergece Chper 13 Reiforceme 1 Corol Cosider lerig o choose cios, e.g., Robo lerig o dock o bery chrger o choose cios o opimize fcory oupu
More informationPure Math 30: Explained!
ure Mah : Explaied! www.puremah.com 6 Logarihms Lesso ar Basic Expoeial Applicaios Expoeial Growh & Decay: Siuaios followig his ype of chage ca be modeled usig he formula: (b) A = Fuure Amou A o = iial
More informationSupplement: Gauss-Jordan Reduction
Suppleme: Guss-Jord Reducio. Coefficie mri d ugmeed mri: The coefficie mri derived from sysem of lier equios m m m m is m m m A O d he ugmeed mri derived from he ove sysem of lier equios is [ ] m m m m
More informationEXPONENTS AND LOGARITHMS
978--07-6- Mthemtis Stdrd Level for IB Diplom Eerpt EXPONENTS AND LOGARITHMS WHAT YOU NEED TO KNOW The rules of epoets: m = m+ m = m ( m ) = m m m = = () = The reltioship etwee epoets d rithms: = g where
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationProject 3: Using Identities to Rewrite Expressions
MAT 5 Projet 3: Usig Idetities to Rewrite Expressios Wldis I lger, equtios tht desrie properties or ptters re ofte lled idetities. Idetities desrie expressio e repled with equl or equivlet expressio tht
More informationInterval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X
ECON 37: Ecoomercs Hypohess Tesg Iervl Esmo Wh we hve doe so fr s o udersd how we c ob esmors of ecoomcs reloshp we wsh o sudy. The queso s how comforble re we wh our esmors? We frs exme how o produce
More information1. Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the
Si ccelerio ecors re show for he cr whose eloci ecor is direced forwrd For ech ccelerio ecor describe i words he iseous moio of he cr A ri eers cured horizol secio of rck speed of 00 km/h d slows dow wih
More informationThe Eigen Function of Linear Systems
1/25/211 The Eige Fucio of Liear Sysems.doc 1/7 The Eige Fucio of Liear Sysems Recall ha ha we ca express (expad) a ime-limied sigal wih a weighed summaio of basis fucios: v ( ) a ψ ( ) = where v ( ) =
More informationLogarithms LOGARITHMS.
Logrithms LOGARITHMS www.mthletis.om.u Logrithms LOGARITHMS Logrithms re nother method to lulte nd work with eponents. Answer these questions, efore working through this unit. I used to think: In the
More informationGraphing Review Part 3: Polynomials
Grphig Review Prt : Polomils Prbols Recll, tht the grph of f ( ) is prbol. It is eve fuctio, hece it is smmetric bout the bout the -is. This mes tht f ( ) f ( ). Its grph is show below. The poit ( 0,0)
More informationAP Calculus AB AP Review
AP Clulus AB Chpters. Re limit vlues from grphsleft-h Limits Right H Limits Uerst tht f() vlues eist ut tht the limit t oes ot hve to.. Be le to ietify lel isotiuities from grphs. Do t forget out the 3-step
More informationMidterm. Answer Key. 1. Give a short explanation of the following terms.
ECO 33-00: on nd Bnking Souhrn hodis Univrsi Spring 008 Tol Poins 00 0 poins for h pr idrm Answr K. Giv shor xplnion of h following rms. Fi mon Fi mon is nrl oslssl produd ommodi h n oslssl sord, oslssl
More informationReleased Assessment Questions, 2017 QUESTIONS
Relese Assessmen Quesions, 17 QUESTIONS Gre 9 Assessmen of Mhemis Aemi Re he insruions elow. Along wih his ookle, mke sure ou hve he Answer Bookle n he Formul Shee. You m use n spe in his ook for rough
More informationEE757 Numerical Techniques in Electromagnetics Lecture 9
EE757 uericl Techiques i Elecroeics Lecure 9 EE757 06 Dr. Mohed Bkr Diereil Equios Vs. Ierl Equios Ierl equios ke severl ors e.. b K d b K d Mos diereil equios c be epressed s ierl equios e.. b F d d /
More informationPhysics 232 Exam I Feb. 14, 2005
Phsics I Fe., 5 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio wih gul eloci o dissec. gie is i ie i is oud o e 8 c o he igh o he equiliiu posiio d oig o he le wih eloci o.5 sec..
More informationProperties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x)
Properies of Logrihms Solving Eponenil nd Logrihmic Equions Properies of Logrihms Produc Rule ( ) log mn = log m + log n ( ) log = log + log Properies of Logrihms Quoien Rule log m = logm logn n log7 =
More informationIntroduction to Matrix Algebra
Itrodutio to Mtri Alger George H Olso, Ph D Dotorl Progrm i Edutiol Ledership Applhi Stte Uiversit Septemer Wht is mtri? Dimesios d order of mtri A p q dimesioed mtri is p (rows) q (olums) rr of umers,
More informationEconomics 8723 Macroeconomic Theory Problem Set 3 Sketch of Solutions Professor Sanjay Chugh Spring 2017
Deparme of Ecoomic The Ohio Sae Uiveriy Ecoomic 8723 Macroecoomic Theory Problem Se 3 Skech of Soluio Profeor Sajay Chugh Sprig 27 Taylor Saggered Nomial Price-Seig Model There are wo group of moopoliically-compeiive
More informationCH 19 SOLVING FORMULAS
1 CH 19 SOLVING FORMULAS INTRODUCTION S olvig equtios suh s 2 + 7 20 is oviousl the orerstoe of lger. But i siee, usiess, d omputers it is lso eessr to solve equtios tht might hve vriet of letters i them.
More informationCH 20 SOLVING FORMULAS
CH 20 SOLVING FORMULAS 179 Itrodutio S olvig equtios suh s 2 + 7 20 is oviousl the orerstoe of lger. But i siee, usiess, d omputers it is lso eessr to solve equtios tht might hve vriet of letters i them.
More informationComparison between Fourier and Corrected Fourier Series Methods
Malaysia Joural of Mahemaical Scieces 7(): 73-8 (13) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: hp://eispem.upm.edu.my/oural Compariso bewee Fourier ad Correced Fourier Series Mehods 1
More informationDividing Algebraic Fractions
Leig Eheme Tem Model Awe: Mlilig d Diidig Algei Fio Mlilig d Diidig Algei Fio d gide ) Yo e he me mehod o mlil lgei io o wold o mlil meil io. To id he meo o he we o mlil he meo o he io i he eio. Simill
More informationMAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPALLI
MAHALAKSHMI EGIEERIG COLLEGE TIRUCHIRAALLI 6 QUESTIO BAK - ASWERS -SEMESTER: V MA 6 - ROBABILITY AD QUEUEIG THEORY UIT IV:QUEUEIG THEORY ART-A Quesio : AUC M / J Wha are he haraerisis of a queueig heory?
More informationSPH3UW Unit 7.5 Snell s Law Page 1 of Total Internal Reflection occurs when the incoming refraction angle is
SPH3UW Uit 7.5 Sell s Lw Pge 1 of 7 Notes Physis Tool ox Refrtio is the hge i diretio of wve due to hge i its speed. This is most ommoly see whe wve psses from oe medium to other. Idex of refrtio lso lled
More informationGlobal alignment in linear space
Globl linmen in liner spe 1 2 Globl linmen in liner spe Gol: Find n opiml linmen of A[1..n] nd B[1..m] in liner spe, i.e. O(n) Exisin lorihm: Globl linmen wih bkrkin O(nm) ime nd spe, bu he opiml os n
More informationPAIR OF LINEAR EQUATIONS IN TWO VARIABLES
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. Two liner equtions in the sme two vriles re lled pir of liner equtions in two vriles. The most generl form of pir of liner equtions is x + y + 0 x + y + 0 where,,,,,,
More informationPhysics 232 Exam II Mar. 28, 2005
Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationONE RANDOM VARIABLE F ( ) [ ] x P X x x x 3
The Cumulive Disribuio Fucio (cd) ONE RANDOM VARIABLE cd is deied s he probbiliy o he eve { x}: F ( ) [ ] x P x x - Applies o discree s well s coiuous RV. Exmple: hree osses o coi x 8 3 x 8 8 F 3 3 7 x
More informationH (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a.
Chpter Review 89 IGURE ol hord GH of the prol 4. G u v H (, ) (A) Use the distne formul to show tht u. (B) Show tht G nd H lie on the line m, where m ( )/( ). (C) Solve m for nd sustitute in 4, otining
More informationECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
More informationANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 2
ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER Seion Eerise -: Coninuiy of he uiliy funion Le λ ( ) be he monooni uiliy funion defined in he proof of eisene of uiliy funion If his funion is oninuous y hen
More informationClass 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference
Thi Film Ierferece Thi- ierferece Ierferece ewee ligh waves is he reaso ha hi s, such as soap ules, show colorful paers. Phoo credi: Mila Zikova, via Wikipedia Thi- ierferece This is kow as hi- ierferece
More informationECSE Partial fraction expansion (m<n) 3 types of poles Simple Real poles Real Equal poles
ECSE- Lecue. Paial facio expasio (m
More informationBEST LINEAR FORECASTS VS. BEST POSSIBLE FORECASTS
BEST LINEAR FORECASTS VS. BEST POSSIBLE FORECASTS Opimal ear Forecasig Alhough we have o meioed hem explicily so far i he course, here are geeral saisical priciples for derivig he bes liear forecas, ad
More informationSection 8 Convolution and Deconvolution
APPLICATIONS IN SIGNAL PROCESSING Secio 8 Covoluio ad Decovoluio This docume illusraes several echiques for carryig ou covoluio ad decovoluio i Mahcad. There are several operaors available for hese fucios:
More informationtwo values, false and true used in mathematical logic, and to two voltage levels, LOW and HIGH used in switching circuits.
Digil Logi/Design. L. 3 Mrh 2, 26 3 Logi Ges nd Boolen Alger 3. CMOS Tehnology Digil devises re predominnly mnufured in he Complemenry-Mel-Oide-Semionduor (CMOS) ehnology. Two ypes of swihes, s disussed
More informationG8-11 Congruence Rules
G8-11 ogruee Rules If two polgos re ogruet, ou ple the oe o top of the other so tht the th etl. The verties tht th re lled orrespodig verties. The gles tht th re lled orrespodig gles. The sides tht th
More informationOne of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of
Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo
More informationBINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =
wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em
More information4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
More informationUnion-Find Partition Structures Goodrich, Tamassia Union-Find 1
Uio-Fid Pariio Srucures 004 Goodrich, Tamassia Uio-Fid Pariios wih Uio-Fid Operaios makesex: Creae a sileo se coaii he eleme x ad reur he posiio sori x i his se uioa,b : Reur he se A U B, desroyi he old
More informationChapter 10. Laser Oscillation : Gain and Threshold
Chaper 0. aser Osillaio : Gai ad hreshold Deailed desripio of laser osillaio 0. Gai Cosider a quasi-moohromai plae wave of frequey propaai i he + direio ; u A he rae a whih
More informationME 501A Seminar in Engineering Analysis Page 1
Seod ad igher Order Liear Differeial Equaios Oober 9, 7 Seod ad igher Order Liear Differeial Equaios Larr areo Mehaial Egieerig 5 Seiar i Egieerig alsis Oober 9, 7 Oulie Reiew las lass ad hoewor ppl aerial
More informationNOTES ON BERNOULLI NUMBERS AND EULER S SUMMATION FORMULA. B r = [m = 0] r
NOTES ON BERNOULLI NUMBERS AND EULER S SUMMATION FORMULA MARK WILDON. Beroulli umbers.. Defiiio. We defie he Beroulli umbers B m for m by m ( m + ( B r [m ] r r Beroulli umbers re med fer Joh Beroulli
More informationHOMEWORK 6 - INTEGRATION. READING: Read the following parts from the Calculus Biographies that I have given (online supplement of our textbook):
MAT 3 CALCULUS I 5.. Dokuz Eylül Uiversiy Fculy of Sciece Deprme of Mhemics Isrucors: Egi Mermu d Cell Cem Srıoğlu HOMEWORK 6 - INTEGRATION web: hp://kisi.deu.edu.r/egi.mermu/ Tebook: Uiversiy Clculus,
More informationGeneral properties of definite integrals
Roerto s Notes o Itegrl Clculus Chpter 4: Defiite itegrls d the FTC Sectio Geerl properties of defiite itegrls Wht you eed to kow lredy: Wht defiite Riem itegrl is. Wht you c ler here: Some key properties
More informationExistence Of Solutions For Nonlinear Fractional Differential Equation With Integral Boundary Conditions
Reserch Ivey: Ieriol Jourl Of Egieerig Ad Sciece Vol., Issue (April 3), Pp 8- Iss(e): 78-47, Iss(p):39-6483, Www.Reserchivey.Com Exisece Of Soluios For Nolier Frciol Differeil Equio Wih Iegrl Boudry Codiios,
More informationFourier transform. Continuous-time Fourier transform (CTFT) ω ω
Fourier rasform Coiuous-ime Fourier rasform (CTFT P. Deoe ( he Fourier rasform of he sigal x(. Deermie he followig values, wihou compuig (. a (0 b ( d c ( si d ( d d e iverse Fourier rasform for Re { (
More informationNotes 03 largely plagiarized by %khc
1 1 Discree-Time Covoluio Noes 03 largely plagiarized by %khc Le s begi our discussio of covoluio i discree-ime, sice life is somewha easier i ha domai. We sar wih a sigal x[] ha will be he ipu io our
More informationElectrical Engineering Department Network Lab.
Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por
More informationUnion-Find Partition Structures
Uio-Fid //4 : Preseaio for use wih he exbook Daa Srucures ad Alorihms i Java, h ediio, by M. T. Goodrich, R. Tamassia, ad M. H. Goldwasser, Wiley, 04 Uio-Fid Pariio Srucures 04 Goodrich, Tamassia, Goldwasser
More information14.02 Principles of Macroeconomics Fall 2005
14.02 Priciples of Macroecoomics Fall 2005 Quiz 2 Tuesday, November 8, 2005 7:30 PM 9 PM Please, aswer he followig quesios. Wrie your aswers direcly o he quiz. You ca achieve a oal of 100 pois. There are
More informationThe limit comparison test
Roerto s Notes o Ifiite Series Chpter : Covergece tests Sectio 4 The limit compriso test Wht you eed to kow lredy: Bsics of series d direct compriso test. Wht you c ler here: Aother compriso test tht does
More informationDepartment of Mathematical and Statistical Sciences University of Alberta
MATH 4 (R) Wier 008 Iermediae Calculus I Soluios o Problem Se # Due: Friday Jauary 8, 008 Deparme of Mahemaical ad Saisical Scieces Uiversiy of Albera Quesio. [Sec.., #] Fid a formula for he geeral erm
More informationLet. Then. k n. And. Φ npq. npq. ε 2. Φ npq npq. npq. = ε. k will be very close to p. If n is large enough, the ratio n
Let The m ( ) ( + ) where > very smll { } { ( ) ( + ) } Ad + + { } Φ Φ Φ Φ Φ Let, the Φ( ) lim This is lled thelw of lrge umbers If is lrge eough, the rtio will be very lose to. Exmle -Tossig oi times.
More informationModeling and Predicting Sequences: HMM and (may be) CRF. Amr Ahmed Feb 25
Modelg d redcg Sequeces: HMM d m be CRF Amr Ahmed 070 Feb 25 Bg cure redcg Sgle Lbel Ipu : A se of feures: - Bg of words docume - Oupu : Clss lbel - Topc of he docume - redcg Sequece of Lbels Noo Noe:
More informationChapter Simpson s 1/3 Rule of Integration. ( x)
Cper 7. Smpso s / Rule o Iegro Aer redg s per, you sould e le o. derve e ormul or Smpso s / rule o egro,. use Smpso s / rule o solve egrls,. develop e ormul or mulple-segme Smpso s / rule o egro,. use
More informationThe Structures of Fuzzifying Measure
Sesors & Trasduers Vol 7 Issue 5 May 04 pp 56-6 Sesors & Trasduers 04 by IFSA Publishig S L hp://wwwsesorsporalom The Sruures of Fuzzifyig Measure Shi Hua Luo Peg Che Qia Sheg Zhag Shool of Saisis Jiagxi
More informationRiemann Integral Oct 31, such that
Riem Itegrl Ot 31, 2007 Itegrtio of Step Futios A prtitio P of [, ] is olletio {x k } k=0 suh tht = x 0 < x 1 < < x 1 < x =. More suitly, prtitio is fiite suset of [, ] otiig d. It is helpful to thik of
More informationm m m m m m m m P m P m ( ) m m P( ) ( ). The o-ordinte of the point P( ) dividing the line segment joining the two points ( ) nd ( ) eternll in the r
CO-ORDINTE GEOMETR II I Qudrnt Qudrnt (-.+) (++) X X - - - 0 - III IV Qudrnt - Qudrnt (--) - (+-) Region CRTESIN CO-ORDINTE SSTEM : Retngulr Co-ordinte Sstem : Let X' OX nd 'O e two mutull perpendiulr
More informatione t dt e t dt = lim e t dt T (1 e T ) = 1
Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie
More information2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)
Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he
More informationAccuplacer Elementary Algebra Study Guide
Testig Ceter Studet Suess Ceter Aupler Elemetry Alger Study Guide The followig smple questios re similr to the formt d otet of questios o the Aupler Elemetry Alger test. Reviewig these smples will give
More informationRight Angle Trigonometry
Righ gl Trigoomry I. si Fs d Dfiiios. Righ gl gl msurig 90. Srigh gl gl msurig 80. u gl gl msurig w 0 d 90 4. omplmry gls wo gls whos sum is 90 5. Supplmry gls wo gls whos sum is 80 6. Righ rigl rigl wih
More informationBig O Notation for Time Complexity of Algorithms
BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time
More informationChemistry 1B, Fall 2016 Topics 21-22
Cheisry B, Fall 6 Topics - STRUCTURE ad DYNAMICS Cheisry B Fall 6 Cheisry B so far: STRUCTURE of aos ad olecules Topics - Cheical Kieics Cheisry B ow: DYNAMICS cheical kieics herodyaics (che C, 6B) ad
More informationHorizontal product differentiation: Consumers have different preferences along one dimension of a good.
Produc Differeiio Firms see o e uique log some dimesio h is vlued y cosumers. If he firm/roduc is uique i some resec, he firm c commd rice greer h cos. Horizol roduc differeiio: Cosumers hve differe refereces
More information( ) 2 3 ( ) I. Order of operations II. Scientific Notation. Simplify. Write answers in scientific notation. III.
Assessmet Ceter Elemetry Alger Study Guide for the ACCUPLACER (CPT) The followig smple questios re similr to the formt d otet of questios o the Aupler Elemetry Alger test. Reviewig these smples will give
More informationHONG KONG INSTITUTE FOR MONETARY RESEARCH
HONG KONG INSTITUTE FOR MONETARY RESEARCH THE GREAT RECESSION: A SELF-FULFILLING GLOBAL ANIC hilippe Bahea ad Eri va Wioop HKIMR Workig aper No.09/03 Jue 03 Hog Kog Isiue for Moeary Researh (a ompay iorporaed
More informationCoefficient Inequalities for Certain Subclasses. of Analytic Functions
I. Jourl o Mh. Alysis, Vol., 00, o. 6, 77-78 Coeiie Iequliies or Ceri Sulsses o Alyi Fuios T. Rm Reddy d * R.. Shrm Deprme o Mhemis, Kkiy Uiversiy Wrgl 506009, Adhr Prdesh, Idi reddyr@yhoo.om, *rshrm_005@yhoo.o.i
More informationDavid Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
More informationOn the Existence and Uniqueness of Solutions for. Q-Fractional Boundary Value Problem
I Joural of ah Aalysis, Vol 5, 2, o 33, 69-63 O he Eisee ad Uiueess of Soluios for Q-Fraioal Boudary Value Prolem ousafa El-Shahed Deparme of ahemais, College of Eduaio Qassim Uiversiy PO Bo 377 Uizah,
More informationECE 102 Engineering Computation
ECE Egieerig Computtio Phillip Wog Mth Review Vetor Bsis Mtri Bsis System of Lier Equtios Summtio Symol is the symol for summtio. Emple: N k N... 9 k k k k k the, If e e e f e f k Vetor Bsis A vetor is
More information0 for t < 0 1 for t > 0
8.0 Sep nd del funcions Auhor: Jeremy Orloff The uni Sep Funcion We define he uni sep funcion by u() = 0 for < 0 for > 0 I is clled he uni sep funcion becuse i kes uni sep = 0. I is someimes clled he Heviside
More informationNumerical Method for Ordinary Differential Equation
Numerical ehod for Ordiar Differeial Equaio. J. aro ad R. J. Lopez, Numerical Aalsis: A Pracical Approach, 3rd Ed., Wadsworh Publishig Co., Belmo, CA (99): Chap. 8.. Iiial Value Problem (IVP) d (IVP):
More informationON BILATERAL GENERATING FUNCTIONS INVOLVING MODIFIED JACOBI POLYNOMIALS
Jourl of Sciece d Ars Yer 4 No 227-6 24 ORIINAL AER ON BILATERAL ENERATIN FUNCTIONS INVOLVIN MODIFIED JACOBI OLYNOMIALS CHANDRA SEKHAR BERA Muscri received: 424; Acceed er: 3524; ublished olie: 3624 Absrc
More informationX-Ray Notes, Part III
oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel
More informationReview Exercises for Chapter 9
0_090R.qd //0 : PM Page 88 88 CHAPTER 9 Ifiie Series I Eercises ad, wrie a epressio for he h erm of he sequece..,., 5, 0,,,, 0,... 7,... I Eercises, mach he sequece wih is graph. [The graphs are labeled
More informationName: Period: Date: 2.1 Rules of Exponents
SM NOTES Ne: Period: Dte:.1 Rules of Epoets The followig properties re true for ll rel ubers d b d ll itegers d, provided tht o deoitors re 0 d tht 0 0 is ot cosidered. 1 s epoet: 1 1 1 = e.g.) 7 = 7,
More informationES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017)
Pae1 Nae Soluios ES 330 Elecroics II Hoework 03 (Fall 017 ue Wedesday, Sepeber 0, 017 Proble 1 You are ive a NMOS aplifier wih drai load resisor R = 0 k. The volae (R appeari across resisor R = 1.5 vols
More informationThe sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.
Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he
More informationF D D D D F. smoothed value of the data including Y t the most recent data.
Module 2 Forecasig 1. Wha is forecasig? Forecasig is defied as esimaig he fuure value ha a parameer will ake. Mos scieific forecasig mehods forecas he fuure value usig pas daa. I Operaios Maageme forecasig
More informationProblem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims
Problem Se 5 Graduae Macro II, Spring 2017 The Universiy of Nore Dame Professor Sims Insrucions: You may consul wih oher members of he class, bu please make sure o urn in your own work. Where applicable,
More informationASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DISCRETE EQUATIONS ON DISCRETE REAL TIME SCALES
ASYPTOTI BEHAVIOR OF SOLUTIONS OF DISRETE EQUATIONS ON DISRETE REAL TIE SALES J. Dlí B. Válvíová 2 Bro Uversy of Tehology Bro zeh Repul 2 Deprme of heml Alyss d Appled hems Fuly of See Uversy of Zl Žl
More informationTaylor Polynomials. The Tangent Line. (a, f (a)) and has the same slope as the curve y = f (x) at that point. It is the best
Tylor Polyomils Let f () = e d let p() = 1 + + 1 + 1 6 3 Without usig clcultor, evlute f (1) d p(1) Ok, I m still witig With little effort it is possible to evlute p(1) = 1 + 1 + 1 (144) + 6 1 (178) =
More information1. Find a basis for the row space of each of the following matrices. Your basis should consist of rows of the original matrix.
Mh 7 Exm - Prcice Prolem Solions. Find sis for he row spce of ech of he following mrices. Yor sis shold consis of rows of he originl mrix. 4 () 7 7 8 () Since we wn sis for he row spce consising of rows
More informationChallenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k
Challenge Problems DIS 03 and 0 March 6, 05 Choose one of he following problems, and work on i in your group. Your goal is o convince me ha your answer is correc. Even if your answer isn compleely correc,
More informationNotes 04 largely plagiarized by %khc
Noes 04 largely plagiarized by %khc Convoluion Recap Some ricks: x() () =x() x() (, 0 )=x(, 0 ) R ț x() u() = x( )d x() () =ẋ() This hen ells us ha an inegraor has impulse response h() =u(), and ha a differeniaor
More informationModule B3 3.1 Sinusoidal steady-state analysis (single-phase), a review 3.2 Three-phase analysis. Kirtley
Module B.1 Siusoidl stedy-stte lysis (sigle-phse), review.2 Three-phse lysis Kirtley Chpter 2: AC Voltge, Curret d Power 2.1 Soures d Power 2.2 Resistors, Idutors, d Cpitors Chpter 4: Polyphse systems
More informationS.E. Sem. III [EXTC] Applied Mathematics - III
S.E. Sem. III [EXTC] Applied Mhemic - III Time : 3 Hr.] Prelim Pper Soluio [Mrk : 8 Q.() Fid Lplce rform of e 3 co. [5] A.: L{co }, L{ co } d ( ) d () L{ co } y F.S.T. 3 ( 3) Le co 3 Q.() Prove h : f (
More information