1998 9 14 1. 1.1 Markov Property 1.2 Wiener Process 1.3 2. 2.1 2.2 2.3 2.4 2.5 2.6 Taylor Expansion 2.7 3. Stochastic 3.1 3.2 SDE(Stochastic Differential Equation) 4. Stochastic 4.1 Stochastic integration 4.2 Ito Integral 4.3 Ito Integral 4.4 5. Ito’s Lemma 5.1 Stochastic 5.1.1 5.1.2 5.1.3 First Order Term Second Order Term Cross Product Terms “ ” – Ito Integral Riemann (Ordinary Differential Equation) (Chain rule) 5.2 Ito’s Lemma 6. 6.1 6.1.1 6.1.2 Closed-Form Solution Numerical Solution
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let f(x) be a quadratic polynomial such that that f(2)= -3 and f(-2)=21‚ then the co-efficient of x in f(x) is a. -3 b. 0 c. -6 d. 2 1. if f(x) =x3 +ax+b is divisible by (x-1) 2 ‚then the remainder obtained when f(x) is divided by (x+2) is ; a. 1 b . 0 c. 3 d. -10 3. the remainder when x1999 is divided
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2008 H I G H E R S C H O O L C E R T I F I C AT E E X A M I N AT I O N Mathematics General Instructions • Reading time – 5 minutes • Working time – 3 hours • Write using black or blue pen • Board-approved calculators may be used • A table of standard integrals is provided at the back of this paper • All necessary working should be shown in every question Total marks – 120 • Attempt Questions 1–10 • All questions are of equal value 212 BLANK PAGE – 2 – Total marks – 120
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THE IMPORTANCE OF MATHEMATICS W. T. Gowers It is with some disbelief that I stand here and prepare to address this gathering on the subject of the importance of mathematics. For a start‚ it is an extraordinary honour to be invited to give the keynote address at a millennium meeting in Paris. Secondly‚ giving a lecture on the significance of mathematics demands wisdom‚ judgment and maturity‚ and there are many mathematicians far better endowed than I am with these qualities‚ including several
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A P P E N D I X E S Tables and Data Sets A Areas under the Normal Curve B Student’s t Distribution C Data Set 1 — Real Estate D Data Set 2 — Major League Baseball E Data Set 3 — OECD F Data Set 4 — Northwest Ohio School Districts G Critical Values of the F Distribution H Critical Values of Chi-Square I Binomial Probability Distribution J Factors for Control Charts K Poisson Distribution L Table of Random Numbers M Wilcoxon T Values N Banking Data Set — Case 262 Appendixes Appendix A Areas
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GRE GRE Now duate ded gra by inten d optioniel major f aM w th the ow wiith score dattS N c ® Guide to the Use of Scores This publication includes: • Guidelines for the use of GRE® scores • Concordance information and percentile ranks oreSele Sc • Score interpretation and statistical information 2012–2013 www.ets.org/gre 19398 CONTENTS The GRE® Board and Its Committees ......................................................................................... 3 Overview of
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Discuss the cause of the Tacoma bridge disaster‚ in terms of waves‚ vibrations‚ and resonance. Elaborate the effects with relevant equations and formulae. The Tacoma bridge collapse can be attributed to the waves caused by the buildup of energetic vibrations. These energetic vibrations were built up from the bridge “taking energy from the steadily blowing wind” (Crowell). Eventually enough of these energetic vibrations built up to cause resonance within the system‚ causing the wave-like motion
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Mathematics is highly valued in our society but for many students the thought of learning mathematics is daunting. Learning mathematics in primacy school may have been a positive experience but it may have also been filled with frustration and anxiety. If a teacher has a negative view of mathematics then their students will adopt this view. Students must be shown the relevance and purpose of mathematics in a real life and meaningful way. There is no doubt that mathematics is an indispensable tool
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Brief Introduction: AJ Davis is a department store chain‚ which has many credit customers and want to find out more information about these customers. AJ Davis has complied a sample of 50 credit customers with data selected in the following variables: Location‚ Income (in $1‚000’s)‚ Size (Number of people living in the household)‚ Years (number of years the customer has lived in the current location)‚ and Credit Balance (customers current credit card balance on the store’s credit car‚ in $)
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Geometry PJ Architecture and Geometry Architecture and geometry are perfect complements of each other they go hand to hand in so many ways let’s discuss some of these ways. Architecture has geometry written all over it if geometry never existed Architecture wouldn’t have existed either. First of all geometry is the reason that we can calculate and measure the sizes and shapes of certain structures for us to use. Geometry allows us pin point exactly how much more we may need or less ‚ without
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