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### LectureFeb15_MATH4321_12S

Course: MATH 4321, Spring 2012
School: HKUST
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Word Count: 1266

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of Reduction a Game in Extensive Form to Strategic Form. Pure strategy. A pure strategy is a players complete plan for playing the game. It should cover every contingency. A pure strategy for a Player is a rule that tells him exactly what move to make in each of his information sets. It should specify a particular edge leading out from each information set. Example: Player I has 3 information sets. The set of...

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HKUST - MATH - 4321
Part II. Two-Person Zero-Sum GamesExample: Odd or EvenPlayers I and II simultaneously call out one of the numbersone or two. Player Is name is Odd; he wins if the sum of thenumbers if odd. Player IIs name is Even; she wins if the sumof the numbers is
HKUST - MATH - 4321
Remark: In the above analysis, we used the basicassumption of Common Knowledge.A fact is common knowledge if everyone knows it, everyoneknows that everyone knows it, everyone knows thateveryone knows that everyone knows it,., and so on adinfinitum.,
HKUST - MATH - 4321
Equilibrium Principle: BR to each otherMaximin Principle: Safety FirstFor Player I: Find p so that MinqpTAq islargest. p is called the Safety Strategy orOptimal Strategy.MinqpTAq is the lower value.For Player II: Find q so that MaxppTAq issmallest.
HKUST - MATH - 4321
Recall that Equilibrium Principle: BR to each other Maximin Principle: Safety firstFor Player I: Find p so that MinqpTAq is largest. p iscalled the Safety Strategy or Optimal Strategy.MinqpTAq is the lower value.For Player II: Find q so that MaxppTA
HKUST - MATH - 4321
MATH 4321Game TheorySpring 2012Assignment 1Exercise I.1.5: 1, 2, 4Exercise I.2.6: 1(a), 1(b), 2, 3, 4Exercise I.3.5:1, 2, 3, 5Exercise I.4.5: 2, 3, 6, 8.Mission : Exercise I.1.5: 6(b), 8.
HKUST - MATH - 4321
MATH 4321Game TheorySpring 2012Assignment 21. Problem II.5.9.1, II.5.9.4.2. The Hidden pearl: There are two dark boxes. Player I hides a pearlin one of them. Then Player II, not knowing which box contains the pearl,peeks into one of them. If the pe
HKUST - MATH - 4321
MATH 310Game TheorySpring 2012Assignment 31. Reduce the Kuhn Tree of Exercise 2 in Assignment 2 to strategic formand then find all PSEs.2. Find the PPSE of the Votes by Veto game in Assignment 2.3. Reduce the following Kuhn tree to strategic form.
HKUST - MATH - 4321
MATH 310Game TheorySpring 2012Assignment 41. Problems II.1.5.1, II.1.5.2, II.1.5.32. Problems II.2.6.2, II.2.6.4, II.2.6.5, II.2.6.6, II.2.6.7, II.2.6.8, II.2.6.103. Prove that for an mxn matrix game, any two saddle points have thesame value.Missi
HKUST - MATH - 4321
MATH 4321Game TheorySpring 2012Assignment 51. Problems II.3.7.3, II.4.7.2, II.5.9.9, II5.9.10(d)2. Solve the following matrix game using the method of linearprogramming.1 31 53. Given a matrix game suppose p1, p2 are optimal strategies for Player
HKUST - MATH - 4321
HKUST - MATH - 102
Math 100 - Introduction to Multivariable CalculusFINAL EXAMINATIONFall Semester, 1999Time Allowed: 2.5 Hours.Total Marks: 100Student Name:Student Number:1. (10 marks) Locate all relative maxima, relative minima and saddlepoints of the functionf (
HKUST - MATH - 102
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HKUST - MATH - 102
Problem 1 (12 points)HKUSTYour Score:MATH 1021(a) If f (x, y ) = (x3 + y 2 ) 3 , nd fx (0, 0) and fy (0, 0).Final ExaminationMultivariable Calculus(b) Let z = f (x, y ), where x = g (t) and y = h(t).(i) Show thatAnswer ALL 8 questionsddtTime
HKUST - MATH - 102
HKUSTMATH 102Final ExaminationMultivariable CalculusAnswer ALL 8 questionsTime allowed 3 hoursProblem 11(a) If f (x, y ) = (x3 + y 2 ) 3 , nd fx (0, 0) and fy (0, 0).(b) Let z = f (x, y ), where x = g (t) and y = h(t).(i) Show thatddtzx= 2
HKUST - MATH - 102
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HKUST - MATH - 102
HKUST - MATH - 102
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HKUST - MATH - 102
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HKUST - MATH - 102
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HKUST - MATH - 102
HKUSTMATH 101Midterm ExaminationProblem 1(a) If e is any unit vector and a an arbitrary vector show thata = (a e)e + e (a e).Multivariable CalculusThis shows that a can be resolved into a component parallel to and one perpendicular to an14 October
HKUST - MATH - 102
Math102 Midterm-2005Problem 1(a) (a b) c = (a c)b (b c)a,i.e. = a c, = b c and = 0.The resulting vector of (a b) c is a linear combination of the vectors a and b, hence it lieson the plane containing the vectors a and b.(b)(i) r = 3.(ii) 0(iii)
HKUST - MATH - 102
HKUSTMATH 102Midterm ExaminationMultivariable and Vector Calculus21 Dec 2005Answer ALL 8 questionsTime allowed 180 minutesDirections This is a closed book examination. No talking or whispering are allowed. Work mustbe shown to receive points. An a
HKUST - MATH - 102
HKUSTMATH 102Midterm ExaminationProblem 1(a) Assume a, b and c are three dimensional vectors and ifMultivariable and Vector Calculus(a b) c = a + b + c.21 Dec 2005Use sux notation to nd , and in terms of the vectors a, b and c. Can you say somethi
HKUST - MATH - 102
HKUSTMATH 102Midterm ExaminationMultivariable and Vector Calculus6 Nov 2006Answer ALL 5 questionsTime allowed 120 minutesDirections This is a closed book examination. No talking or whispering are allowed. Work mustbe shown to receive points. An an
HKUST - MATH - 102
HKUSTMATH 102Second Midterm ExaminationMultivariable and Vector Calculus15 Dec 2006Problem 1(a) x + 2y z = 10(b) x2 + (y 1)2 + z 2 = 1which is the equation of a sphere with center (0, 1, 0) and radius 1.(c) The distance between two planes isd =
HKUST - MATH - 102
HKUSTMATH 102Second Midterm ExaminationMultivariable and Vector Calculus15 Dec 2006Answer ALL 8 questionsTime allowed 180 minutesProblem 1(a) Find an equation of the plane through (1, 4, 3) and perpendicular to the linex = t + 2,y = 2t 3,z = t.
HKUST - MATH - 102
HKUSTMATH 102Third Midterm ExaminationMultivariable and Vector Calculus12 April 2007Answer all ve questionsTime allowed 120 minutesDirections This is a closed book examination. No talking or whispering are allowed. Workmust be shown to receive poi
HKUST - MATH - 102
Problem 1 (20 points)HKUSTYour Score:MATH 102Identify the following surfacesMidterm One Examination(a) r u = 0.Multivariable and Vector Calculus(b) (r a) (r b) = k .30 Oct 2007(c)r (r u)u = k . [Hint: What are the vectors (r u)u and r (r u)u?]
HKUST - MATH - 102
HKUSTMATH 102Midterm One ExaminationMultivariable and Vector CalculusProblem 4(a) Find the parametric equation of the curve of intersection C between the plane z = 2y + 3and the surface z = x2 + y 2 . Find also the equation of the projection curve o
HKUST - MATH - 102
HKUSTMATH 102Third Midterm ExaminationMultivariable and Vector Calculus12 April 2007Answer all ve questionsTime allowed 120 minutesDirections This is a closed book examination. No talking or whispering are allowed. Workmust be shown to receive poi
American University in Cairo - EENG - 320
Signals and Systems (EENG 320)Assignment (5)1. Use either the Fourier transform analysis and synthesis equations or theFourier transform properties to:a. Compute the Fourier transform of each of the following signals:i. [e t cos(o t )]u (t ), &gt; 0ii.
American University in Cairo - EENG - 320
American University in Cairo - EENG - 320
Signals and Systems (EENG 320)Assignment (4)1- Determine the Fourier series representation for the following signals:i. x(t ) periodic with period 2 andx(t ) = e tfor - 1 &lt; t &lt; 1ii. Each x(t ) illustrated in figures (1)-(3).x(t)1-5-3-4-1153
American University in Cairo - EENG - 320
Signals and Systems (EENG 320)Assignment (3)1) Compute the convolution y[ n] = x[ n] h[ n] of the following signals :x[n] = nu[n]y[n] = nu[n], 2) Compute the convolution y (t ) = x (t ) h(t ) of the following signals, sketch the result:x (t ) = e t
American University in Cairo - EENG - 320
Signals and Systems (EENG 320)Assignment (2)1) Consider a continuous time signal :x (t ) = (t + 2) (t 2)If a signal :2ty (t ) = x( )da. Is y(t) an energy signal or power signal?b. Calculate its energy and power2) Consider the discrete time signa
American University in Cairo - EENG - 320
Signals and Systems (EENG 320)Assignment (1)fig(1)fig(2)1) A continuous-time signal x(t) is shown in fig(1). Sketch and label carefully each of thefollowing signals: The original signal x(t)a. x(t-1)b. x(2-t)c. x(2t+1)d. x(4-t/2)e. [x(t) + x(-t)
American University in Cairo - EENG - 320
Signals and Systems (EENG 320)Assignment (1)fig(1)fig(2)1) A continuous-time signal x(t) is shown in fig(1). Sketch and label carefully each of thefollowing signals:a. x(t-1)b. x(2-t)c. x(2t+1)d. x(4-t/2)e. [x(t) + x(-t)] u(t)f. x(t) [ (t+2/3)
CHAPTER 22.1DYNAMIC MODELS AND DYNAMIC RESPONSERevisiting Examples 2.4 and 2.5 will be helpful.(a)R (s) = A;Y ( s) =y(t ) =(b)KA - t / te;tR(s) =A;sKAt s +1yss = 0Y(s) =KAs (s + 1)y(t) = KA (1 e t / ) ;(c)R(s) =yss = KAAKA; Y(
IIT Kanpur - STATISTICS - SI406
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IIT Kanpur - STATISTICS - SI406
SI515 (Autumn 2010) Assessment of Solutions of Assignment 1Common Mistakes/Flaws:C1: Quantitative Feature Values are NOT normalized.C2: How the training sample was selected randomly from the given data is NOTSpecified/justified.C3: Your own code and/
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Department of Mathematics, IIT BombaySI 515 (Data Mining): Autumn 2010Assignment Sheet-IIEvery question is a Test Assignment for individual groups and carries max. of 10 marks.Q1. Make clusters of Fishers iris data using (i) suitable 0-1 Integer progr
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Chapter 2The Backprop AlgorithmCopyright 1995 by Donald R. Tveter, drt@christianliving.net. Commercial UseProhibited2.1 Evaluating a NetworkFigure 2.1 shows a simple back-propagation network that computes the exclusive-or(xor) of two inputs, x and y
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Biostatistics 695 HW # 3Jian KangOctober 3, 20072.7 In the United States, the estimated annual probability that a woman over the ageof 35 dies of lung cancer equals 0.001304 for current smokers and 0.000121 fornonsmokers (M. Pagano and K. Gauvreau, P
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Mathematical Geology, Vol. 14, No. 6, 1982U se of the Bray-Curtis Similarity Measure inCluster Analysis of Foraminiferal Data jMichael G. Michie 2Transformation of data effectively limits the distortion by outlying values on the BrayCurtis similarity
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