Pierre Fermat’s father was a wealthy leather merchant and second consul of Beaumont- de- Lomagne. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. Although there is little evidence concerning his school education it must have been at the local Franciscan monastery. He attended the University of Toulouse before moving to Bordeaux in the second half of the 1620s. In Bordeaux he began his first serious mathematical researches and in 1629 he gave a
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1.INTRODUCTION: The mathematician Diophantus of Alexandria around 250A.D. started some kind of research on some equations involving more than one variables which would take only integer values.These equations are famously known as “DIOPHANTINE EQUATION”‚named due to Diophantus.The simplest type of Diophantine equations that we shall consider is the Linear Diophantine equations in two variables: ax+by=c‚ where a‚b‚c are integers and a‚b are not both zero. We also have many kinds of Diophantine
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Normal Distribution It is important because of Central Limit Theorem (CTL)‚ the CTL said that Sum up a lot of i.i.d random variables the shape of the distribution will looks like Normal. Normal P.D.F Now we want to find c This integral has been proved that it cannot have close form solution. However‚ someone gives an idea that looks stupid but actually very brilliant by multiply two of them. reminds the function of circle which we can replace them to polar coordinate Thus Mean
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5/3/2011 Lecture 1 LECTURE 1 TOPICS I. Product of Inertia for An Area Definition Parallel Axis Theorem on Product of Inertia Moments of Inertia About an Inclined Axes Principal Moments of Inertia Mohr’s Circle for Second Moment of Areas II. Unsymmetrical Bending II Unsymmetrical Bending Unsymmetrical Bending about the Horizontal and Vertical Axes of the Cross Section Unsymmetrical Bending about the Principal Axes 1 5/3/2011 Lecture 1‚ Part 1 Product of Inertia for an Area
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two major branches‚ differential calculus (concerning rates of change and slopes of curves)‚ and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-definedlimit. Calculus has widespread uses in science‚ economics‚ and engineering and can solve many problems that algebra alone
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bonds calculation of yield to call for bonds calculation of current yield/capital gains yield for bonds calculation of coupon interest rate/PMT for bonds effect of change in interest rates on price of bonds Bond sensitivities/Bond theorems calculation of capital gains yield calculation of expected total return using expected dividends‚ stock price and growth rate calculation of stock price using expected total return‚ expected dividends/current dividends‚ and growth rate
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with a sample size of 120‚ the test with the highest rejection rates are Horizontal and Vertical Difference‚ Maximum Variation Rates‚ and Mean Variation Rates. The data for the three tests is evenly distributed therefore; “applying the Central Limit Theorem‚ researchers can conclude that the behavior sample represents the behavior of the population” (section 2). As a result of the tests‚ upgrading the Timing and Poising machines as well as purchasing Customized Movement Holders to aid in securing the
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A project assessment study based on the combination of the CAPM model and the MM theory Dilina Kuerban (FIN620 Long-term financial management) 11/15/2014 Abstract 1. Modigliani- Miller theorem……………………….......………..….……………… (1)Modigliani and Miller Proposition --No tax scenario…………………………… (2)Modigliani and Miller Proposition--with taxes scenario………………………… 2. Combination of CAPM model and MM theory………………………………….. 3. A case study……………………………………………………………………….... 4. Limitation of combination
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Math/Stat 394‚ Winter 2011 F.W. Scholz Central Limit Theorems and Proofs The following gives a self-contained treatment of the central limit theorem (CLT). It is based on Lindeberg’s (1922) method. To state the CLT which we shall prove‚ we introduce the following notation. We assume that Xn1 ‚ . . . ‚ Xnn are independent random variables with means 0 and 2 2 respective variances σn1 ‚ . . . ‚ σnn with 2 2 2 σn1 + . . . + σnn = τn > 0 for all n. 2 Denote the sum Xn1 + . . . + Xnn by Sn and observe
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Tutorial 07: Solutions Part A: For all your answers‚ please remember to do the following: 1. Draw curves 2. State the distribution 3. Define the variable A7.1 An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed‚ with mean µ = 117 cm and standard deviation σ = 2.1 cm. If the machine is operating correctly: Let X = variable length of subcomponent (cm). Then if the machine is operating correctly‚ X ~ N (117‚ 2.12
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