Statistics and parameters. Properties for a statistic. Central Limit Theorem. Distribution of the sample mean‚ difference in means and the proportion. Point and interval estimates for the mean‚ difference in means‚ and proportion. Hypotheses testing and types of errors. Significance levels and p values. Small sample testing: Chi square‚ t and F distributions and their properties. Applications of chi square and t distributions to interval estimates and tests. UNIT 2 : CLASSICAL TWO VARIABLE LINEAR
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Mathematics in Indian has a very long and hallowed record. Sulvasutras‚ the most ancient extant written sms messages (prior to 800 BCE) that deal with mathematics‚ clearly situation and make use of the so-called Pythagorean theorem apart from providing various exciting estimates to surds‚ in connection with the development of altars and fire-places of different forms and designs. By enough duration of Aryabhata (c.499 CE)‚ the Native indian specialised mathematicians were completely acquainted with
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The ancient Greek civilization had many contributions that helped explain its significance in history. During the Archaic Age‚ there were many economies and cultures. One economy were the coins. Although‚ the Greeks did not invent coins they did use coins to their advantage. They improved the design of the coins and the circulation of them. The Greeks added stamps to both sides of the coins for identification and made them of silver (Dutton 48). The Greeks used the coins for “collection of taxes
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Reprinted with corrections from The Bell System Technical Journal‚ Vol. 27‚ pp. 379–423‚ 623–656‚ July‚ October‚ 1948. A Mathematical Theory of Communication By C. E. SHANNON T I NTRODUCTION HE recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist 1 and Hartley2 on this subject
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A Beautiful Mind is a story based on the life of the famous mathematician John Forbes Nash‚ Jr. His contributions to mathematics are outstanding. When he was an undergraduate‚ he proved Brouwer’s fixed point theorem. He then broke one of Riemann’s most perplexing mathematical problems and became famous for the Nash Solution. Game Theory from then on‚ Nash provided breakthrough after breakthrough in mathematics. In 1958 John Forbes Nash was described as being ’the most promising young mathematician
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by friction‚ and the network. (d) Repeat the calculation if the applied force is exerted at an angle of 30.0° with the horizontal. Kinetic Energy and the Work–Energy Theorem The kinetic energy KE of an object of mass m moving with a speed v is defined by KE = ½ mv2 SI unit: joule ( J ) = kgm2/s2 The work–energy theorem states that the net work done on an object of mass m is equal to the change in its kinetic energy‚ or Wnet = KEf - KEi = Fd where the change in the kinetic energy is due
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205 How could you use Descartes’ rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial? | Descartes rule is really helpful because it eliminates the long list of possible rational roots and you can tell how many positives or negatives roots you will have. Fundamental Theorem of Algebra finds the maximum number of zeros which includes real and complex numbers
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(3) Pyro electric (4) Magneto optic Where K and s are thermal and electrical conductivities in a solid‚ according to Wiedemann Franz law 1. The theorem used for equilibrium of concurrent 8. coplanar forces is (1) Varignon’s Theorem (2) Lame’s Theorem (3) Parallel Axis Theorem 9. (4) Perpendicular Axis Theorem 2. 3. Tangential acceleration of the body moving with constant velocity on a curve is equal to KT K s (1) = constant (2) = constant 2 s
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Data Depth and Optimization Komei Fukuda fukuda@ifor.math.ethz.ch Vera Rosta rosta@renyi.hu In this short article‚ we consider the notion of data depth which generalizes the median to higher dimensions. Our main objective is to present a snapshot of the data depth‚ several closely related notions‚ associated optimization problems and algorithms. In particular‚ we briefly touch on our recent approaches to compute the data depth using linear and integer optimization programming. Although
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Purdue University Purdue e-Pubs Computer Science Technical Reports Department of Computer Science 1993 A Geometric Constraint Solver William Bouma Ioannis Fudos Christoph M. Hoffmann Purdue University‚ cmh@cs.purdue.edu Jiazhen Cai Robert Paige Report Number: 93-054 Bouma‚ William; Fudos‚ Ioannis; Hoffmann‚ Christoph M.; Cai‚ Jiazhen; and Paige‚ Robert‚ "A Geometric Constraint Solver" (1993). Computer Science Technical Reports. Paper 1068. http://docs.lib.purdue.edu/cstech/1068
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