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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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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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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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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Puzzle: Who Got More? Mrs Mess was buying a set of garden furniture. The bill was seventy rupees. She gave the attendant what she thought were two ₹50 notes‚ (actually two ₹100 notes). The attendant was sleepy and didn’t notice either‚ so he gave Mrs Mess what he thought were three ₹10 notes (actually three ₹50 notes). Who ended up better off than they should? Solution: Mrs Mess comes away better off than she should‚ by ₹20 in fact. Despite the warning in the title‚ Mrs Mess did pay
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TEST BANK > CONTROL PANEL > POOL MANAGER > POOL CANVAS Pool Canvas Add‚ modify‚ and remove questions. Select a question type from the Add Question drop-down list and click Go to add questions. Use Creation Settings to establish which default options‚ such as feedback and images‚ are available for question creation. Add Creation Settings Name Chapter 1--Fundamental Concepts Description Instructions Modify Add Question Here Multiple Choice 0 points Modify Remove Question Which of the following
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Article 1: Titre: Colorado Flooding Imperils Oil and Gas Sites‚ Causes Spill Date: Septembre 19‚ 2013 Journal : National Geographic Cet article parle de l’inondation à Colorado le 17 Septembre‚ 2013. Cette inondation était un grand désastre parce qu’il y avait un grand déversement de pétrole. Il y avait a peu près 5250 gallons de pétrole qui a infiltré la rivière South Platte dans la partie centre-nord de l’état. Le pétrole venait des réservoirs pétroliers Anadarko endommagés. Cette déversement
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