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### Math543_syl

Course: MATH 5010, Spring 2011
School: HKU
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543: MATH Advanced Mathematical Statistics I Academic Year 20102011, Fall Semester Instructor: Dr. Bing-Yi JING. Email: majing@ust.hk. Room: 3489. Phone: 2358 7458. Main References: 1. Mathematical Statistics by J. Shao. 2. Theory of Point Estimation by E.L. Lehmann. 3. Statistical Inference, by G. Casella and R. L. Berger. Contents: course This is concerned with the theory of statistical inference in Point...

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543: MATH Advanced Mathematical Statistics I Academic Year 20102011, Fall Semester Instructor: Dr. Bing-Yi JING. Email: majing@ust.hk. Room: 3489. Phone: 2358 7458. Main References: 1. Mathematical Statistics by J. Shao. 2. Theory of Point Estimation by E.L. Lehmann. 3. Statistical Inference, by G. Casella and R. L. Berger. Contents: course This is concerned with the theory of statistical inference in Point Estimation. Topics include: suciency, ancillary statistics, completeness, UMVU estimators, information inequality, eciency, asymptotic maximum likelihood theory, average risk optimality, minimaxity and admissibility. Assessment: Assignments: 20%. Final: 80%. 1
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HKU - MATH - 5010
MAFS 501: Stochastic CalculusSome of the questions in previous nal examinations=The following facts might be useful to you.ttHs dXs ,tKs dYs =0Hs K s d X , Y0s.0 Levys Characterization of Brownian motion:Mt is a BM i Mt is a continuous mart
HKU - MATH - 5010
Solution to Homework 11. What is the distribution of Bs + Bt , s t?Solution. E (Bs +Bt ) = 0, var(Bs +Bt ) = var(Bs )+var(Bt )+2E (Bs Bt ) = s+t+2s =3s + t. So Bs + Bt N (0, 3s + t).2. Compute E [Bt1 Bt2 Bt3 ] for t1 &lt; t2 &lt; t3 .Solution. Let with 0 =
HKU - MATH - 5010
0.1Exercises1. A function, f , is said to be Lipschitz-continuous on [0, T ] if there exists a constantC &gt; 0 such that for any t, t [0, T ],|f (t) f (t )| &lt; C |t t |.Show that a Lipschitz-continuous function has bounded variation and zero 2-variation
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesHomework FiveCourse Instructor: Prof. Y.K. Kwok1. Consider a European capped call option whose terminal payo function is given bycM (S, 0; X, M ) = min(max(S X, 0), M ),where X is the strike pr
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesHomework FourCourse Instructor: Prof. Y.K. Kwok1. Consider the Brownian motion with drift dened byX (t) = t + Z (t),X (0) = 0, Z (t) is the standard Brownian motion,nd E [X (t)|X (t0)], var(X
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesHomework OneCourse Instructor: Prof. Y.K. Kwok1. Consider a one-year forward contract whose underlying asset is a coupon paying bond with maturitydate beyond the expiration date of the forward c
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesHomework ThreeCourse Instructor: Prof. Y.K. Kwok1. Consider the sample space = cfw_3, 2, 1, 1, 2, 3 and the algebra F = cfw_, cfw_3, 2,cfw_1, 1, cfw_2, 3, cfw_3, 2, 1, 1, cfw_3, 2, 2, 3, cfw_1,
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesHomework TwoCourse Instructor: Prof. Y.K. Kwok1. Show that a dominant trading strategy exists if and only if there exists a trading strategy satisfying V0 &lt; 0and V1 () 0 for all .Hint: Consider
HKU - MATH - A
MAFS 5030 - Quantitative Modeling of Derivatives SecuritiesSolution to Homework Four1. (a) It is easily seen thatt+sk2X1 (t + s) X1 (s) = k Zsk2Z+is normally distributed with mean zero and variance k 2 tk2s ks2 = t. Alsothe increments X1 (ti+1
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesSolution to Homework OneCourse Instructor: Prof. Y.K. Kwok1. There will be two coupons before delivery: one in 6 months and one just prior todelivery. Using the present value formula:\$94.6 =F
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesSolution to Homework ThreeCourse Instructor: Prof. Y.K. Kwok1. F is generated by the partition P = cfw_3, 2, cfw_1, 1, cfw_2, 3.(i) Since cfw_2, 3 P and X (2) = 4 = X (3) = 9, X is not F -measur
HKU - MATH - A
MAFS 5030Quantitative Modeling of Derivatives SecuritiesSolution to Homework TwoCourse Instructor: Prof. Y.K. Kwok1. part: The trading strategy H with V0 &lt; 0 and V1 ( ) 0, , dominates the zero-holding trading strategy H = (0 0 0)T . The zeroholding st
Iowa State - EE - 230
CE1N4001 THRU 1N4007CHENYI ELECTRONICSGENERAL PURPOSE PLASTIC RECTIFIERReverse Voltage - 50 to 1000 VoltsForward Current - 1.0AmpereFEATURES. The plastic package carries Underwrites LaboratoryFlammability Classification 94V-0. Construction utiliz
Iowa State - EE - 230
oHVE S COAV R MAI SIO PLLA N IABL S NTE*RFeaturesLead free versions available (see How toOrder Termination option)RoHS compliant (lead free version)*Compatible with automatic insertionequipmentSuperior package integrityMarking on contrastin
Iowa State - EE - 230
Agilent E363xA Series Programmable DC Power SuppliesData SheetReliable Power, Repeatable ResultsSingle and triple output 80 W to 200 W output power Dual range output (except E3631A) Low noise and excellent regulation Remote sensing (except E3631A) Fron
Iowa State - EE - 230
Users GuidePublication Number 33220-90002 (order as 33220-90100 manual set)Edition 4, May 2007Copyright 2003, 2005, 2007 Agilent Technologies, Inc.Agilent 33220A20 MHz Function /Arbitrary Waveform GeneratorAgilent 33220A at a GlanceThe Agilent Tec
Iowa State - EE - 230
Agilent 33220A 20 MHzFunction/ArbitraryWaveform GeneratorData Sheet20 MHz Sine and Square waveformsPulse, Ramp, Triangle, Noise, and DC waveforms14-bit, 50 MSa/s, 64 K-point Arbitrary waveformsAM, FM, PM, FSK, and PWM modulation typesLinear &amp; loga
Iowa State - EE - 230
Agilent 34410A/11A 6 Digit Multimeter(includes the L4411A 1U DMM)Users GuideAgilent TechnologiesNotices Agilent Technologies, Inc. 2005, 2006, 2007 No part of this manual may be reproduced in any form or by any means (including electronic storage and
Iowa State - EE - 230
Agilent 4263B LCR MeterOperation ManualSERIAL NUMBERSThis manual applies directly to instruments which hasthe serial number prex JP1KD, or rmware revision 1.0.For additional important information about serialnumbers, read \Serial Number&quot; in Appendix
Iowa State - EE - 230
Agilent 4263B LCR MeterUser's GuideAgilent Part No. 04263-90022Printed in JAPANDecember 2000Fourth EditionDocumentation MapUser's Guide( This bookIs a handy reference to help you to get started using your 4263B, basic measurements andcommonly u
Iowa State - EE - 230
D igital Phosphor OscilloscopesD PO3000 SeriesFeatures &amp; BenefitsKey PerformanceSpecifications 500, 300, 100 MHzbandwidth models 2 and 4 channel models Sample rates up to 2.5 GS/son all channels 5 megasample record lengthon all channels 50,000
Iowa State - EE - 230
Iowa State - EE - 230
y lppuS rewoP CD tuptuO elpirT A1363E tneligA. d e v r e s e R st h gi R ll A 7002-0002 .cnI ,seigolonhceT tneligA thgirypoC .xednI eht dniheb segap eht ees ,noitamrofni yrotalugeR dna ,seitnarraW ,noitamrofni ytefaS roF.7002 rebotcO 20009-1363E :rebmuN
Keller Graduate School of Management - FINANCIAL - f1515
F1515 Homework 3 Tasha Smith 5-1 Bond Valuation with Annual payments Jackson Corporation's bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a \$1,000 par value, and the coupon interest rate is 8%. The bonds have a yield
Iowa State - EE - 230
EE 230 Exam 1 Spring 2010NAME _Instructions: The points allocated to each problem on this exam are as indicated. All work should be included on the exam itself. Attach additional sheets only if you run out of space on a problem. Students may bring 1 pag
Keller Graduate School of Management - FINANCIAL - f1515
F1515 Homework 4 Tasha Smith (72) Constant Growth Valuation Boehm Incorporated is expected to pay a \$1.50 per share dividend at the end of this year (i.e., D1 = \$1.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of
Keller Graduate School of Management - FINANCIAL - f1515
Pages 210 - 211 5.1 Jackson Corporation's bonds have 12 years remaining to maturity. Interest is paid annually.? Jackson Corporation's bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a \$1,000 par value, and the coupon
Iowa State - EE - 230
EE 230 Exam 2 Spring 2010NAME _Instructions: There are 8 short questions and 5 problems. The points allocated to each of the questions are as indicated. The problems are all equally weighted with an assigned weight of 16 points each. All work should be
Keller Graduate School of Management - FINANCIAL - f1515
Project p. 460 11-7 You have been asked by the president of your company to evaluate the proposed acquisition of a new spectrometer for the firm's R&amp;D department. The equipment's basic price is \$70,000, and it would cost another \$15,000 to modify it for s
Iowa State - EE - 230
EE 230Exam 3Spring 2010NAME _Instructions: There are 8 short questions and 5 problems. The points allocated to each ofthe questions are as indicated. The problems are all equally weighted with an assignedweight of 16 points each. All work should be
Keller Graduate School of Management - FINANCIAL - f1515
Fi-515-Week5 1. What is the net cost of the spectrometer-Year 0 net cash flow? Basic Price-\$70,000 Modification-\$15,000 Increase Working Capital-\$4,000 Total-\$89,000=(89,000)-Outflow 2. Net operating cash flows Years 1, 2, 3. Total amount of depreciation-
Keller Graduate School of Management - FINANCIAL - f1515
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Iowa State - EE - 230
EE 230 Final Exam Fall 2006NAME _Instructions: There are 8 short questions and 8 problems. The points allocated to each of the questions are as indicated. The problems are all equally weighted with an assigned weight of 10 points each. All work should b
Keller Graduate School of Management - FINANCIAL - f1515
Hewlett-Packard 12C TutorialTo begin, look at the face of the calculator. Every key (except the arithmetic function keys in the far right column and the five keys on the bottom left row) has two or three functions: each key's primary function is noted in
Iowa State - EE - 230
EE230: Solution to Homework Assignment 1 Problem 1 a. Marvell Technology Group b. 2.3B Marvell Vs 15 Billion Iowa corn and soybean c. Market Capitalization: 12.72B (January 2010) Problem 2 a. Paul Gray b. Abstract A pipelined, 13-bit, 250-ksample/s (ks/s)
Keller Graduate School of Management - FINANCIAL - f1515
Hewlett-Packard 17BII TutorialTo begin, look at the face of the calculator. Most keys on the 17BII have two functions: a key's primary function is noted in white on the key itself, while each key's secondary function is noted in gold above the key. To us
Keller Graduate School of Management - FINANCIAL - f1515
MANAGERIAL FINANCE PROJECT #2 13-10 A. 1. Net Operating Profit after Taxes (Operating Income x (1-Tax Rate) NOPAT for 2011 = 108.6 (1-.40)=\$65.16 2. Net Operating Working Capital for 2011 is calculated through Taking your Current Assets less Non-Interest
Iowa State - EE - 230
EE 230 Homework Assignment 1 Spring 2010Problem 1. Departmental alum, Sehat Sutardja (BSEE 1983) started a semiconductor company after a short stint in industry. a) What is the name of the company he co-founded? b) How do the annual sales of this company
Keller Graduate School of Management - FINANCIAL - f1515
Midterm wk 4 1. Question : (TCO A) Wages paid to an assembly line worker in a factory are a: Student Answer: Prime Cost YES.Conversion Cost NO CORRECT Prime Cost YES.Conversion Cost YES Prime Cost NO.Conversion Cost NO Prime Cost NO.Conversion Cost YES In
Iowa State - EE - 230
EE 230 HW2 Solutions Problem 1 1. A square wave can be represented a sum of an infinite number of sine waves as follows:xsquare4k1sin 2 ft 2k 1 2k 1a. When K=1 , we obtain the fundamental b. When K=2,.,7 , we obtain the 2nd,3rd, .,7th harmonics respe
Keller Graduate School of Management - FINANCIAL - f1515
Wednesday, September 28, 2011 Answer to A, B, and C submitted by Vanessa Munoz FI515_Course Project_Vanessa_Munoz A.) Estimated Investment Requirements: Price \$-70,000 Modification -15,000 Change in net working capital -4,000 Total investment \$-89,000 B.)
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EE 230 Assignment 2 Spring 2009 Problem 1 Plot two periods of square wave that is symmetric with respect to the horizontal axis with peak value of 1 volt and a period of 1 sec. On the same axis, plot a) the fundamental b) the first 7 harmonics c) the sum
Keller Graduate School of Management - FINANCIAL - f1515
Week 5 project Problem 11- 7 &quot;New-Project Analysis&quot; You have been asked by the president of your company to evaluate the proposed acquisition of a new spectrometer for the firm's R&amp;D department. The equipment's basic price is \$70,000, and it would cost an
Keller Graduate School of Management - FINANCIAL - f1515
My Project Homework Assignment Week 5 10-8 NPV IRRs and MIRRs for Independent Projects Edelmann is considering including two pieces of equipment, a truck and an overhead pulley system, in this year's capital budget. The projects are independent. The cash
Iowa State - EE - 230
EE 230 Assignment 3 Spring 2010 Problem 1 A system has a transfer function with no zeros, a single pole at s = -6, and a dc gain of 9. a) Write the transfer function b) Determine the response to a step of 5u(t). Assume the output prior to t =0 is 0. Probl
Keller Graduate School of Management - FINANCIAL - f1515
Iowa State - EE - 230
EE 230 Homework 4 Spring 2010Problem 1 Three networks are shown along with the type of A amplifier if this is to be used in a standard feedback network. Determine the value of in all three cases. You may assume the port impedances of the A amplifier are
Iowa State - EE - 230
Matlab codeclear all close all f= -2:.01:5; f=10.^f; w=2*pi*f; T = 5000./sqrt(w.^2 + 10^6); semilogx(f,T,'linewidth',2.5) grid on xlabel('Frequency(Hz)','fontsize',14),ylabel('Magnitude','fontsize',14) set(get(gcf,'CurrentAxes'),'FontSize',14) title('Mag
Iowa State - EE - 230
EE 230 Homework Assignment 5 Spring 2010 . Problem 1 Determine the output variable (in the s-domain) indicated. Assume the op amps are ideal.Problem 2 Determine the 3-dB band edge for the following circuit and plot the magnitude of the transfer function.
Iowa State - EE - 230
EE 230 Homework Assignment 6 Spring 2010Problem 1Consider the basic noninverting feedback amplifier circuit where the R nominal dc gain is given by the expression K 0 =1+ 2 . R1 A BWA a) Assuming the gain of the op amp is given by A1 ( s ) = 0 s+BWA Sho
Iowa State - EE - 230
clear all close all time = -2:0.01:2; % 8 seconds gives us 8 cycles Vin = [(4*time(1:99)+6),(4*time(100:199)+2),(4*time(200:299)2),(4*time(300:401)-6)]; % part a % Vout2 = -2*Vin; Vout1 = 10*(Vin&gt;31/20)-10*(Vin&lt;31/20);figure(1) plot(time,Vin,'b','linewid
Iowa State - EE - 230
EE 230 Homework 7 Spring 2010 Note: This homework assignment has a mixture of some problems that are quite straightforward and some that are quite challenging. Target solving at least 75% of the problems. Anything over 75% should be viewed as Extra Credit
Iowa State - EE - 230
EE 230 Homework 8 Spring 2010 (Note: Since there is an Exam on Friday March 12, this assignment will not be collected but solutions will be posted)Problem 1 The circuit shown is a comparator with hysteresis. In this circuit, assume R2=10K and R1=100 a) D
Iowa State - EE - 230
EE 230HW 9Spring 2010Problem 1Determine analytically and plot the transfer characteristics of thefollowing circuit if the Nonlinear Device (NLD) can be modeled with the I-Vfor VD 0I = 0characteristics D. The transfer characteristics of the NLD ar
Iowa State - EE - 230
EE 230Homework 10Spring 2010Problem 1Assume the transistor M2 shown below is characterized by the model onthe last page of this HW assignment. Determine IX.Problem 2If the Op Amp is ideal and R2=50K, determine the gain of the amplifier ifVCONT=4V.