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Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent...

Topics: probability, probability models, bayes rule, discrete random variables, continuous random...

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Mar 1, 2018
03/18

by
MIT OpenCourseWare

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View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis,Â Patrick Jaillet The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management. This resource is a companion site to 6.041SC Probabilistic Systems Analysis and Applied Probability. It covers the same content, using...

Topics: RES.6-012, RES.6, probability, probability models, bayes rule, discrete random variables,...

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Aug 17, 2013
08/13

by
E. S. Wentzel

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The author of this booklet describes in popular language how probability theory was developed and found wide application in all fields of modern science. This book can be considered as an introduction towards a more thorough study of probability theory and is intended for a wide circle of readers.

Topics: mathematics, statistics, propability, chance, random variables, frequency, applications

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Apr 27, 2018
04/18

by
A. D. MyÅ¡kis

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In this post, we will see the bookÂ Introductory Mathematics for Engineers: Lectures in Higher MathematicsÂ by A. D. My Å¡ kis. About The Book The present book is based on lectures given by the authorÂ overÂ a number of years to students of various engineering and physics. The book includes some optional can be skipped for the first reading. The corresponding Items m the table of contents are marked by an asterisk. ... The book is composed in such a way that it is possible to use it both for...

Topics: mir books, mathematics, higher, variables, functions, graphs, analytic geometry, limits, continuity...

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Jul 11, 2010
07/10

by
NON

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The proceedings of a conference on electric storage batteries are presented. The subjects discussed include the following: (1) a low cost/standardization program, (2) test and flight experience, (3) materials and cell components, and (4) new developments in the nickel/hydrogen system. The application of selected batteries in specific space vehicles is examined.

Topics: BOUNDARY LAYER TRANSITION, LAMINAR BOUNDARY LAYER, TURBULENT BOUNDARY LAYER, WIND TUNNEL WALLS,...

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A lot of events in our life seem random or impossible to predict. However, with probability theory we can learn more about these things to solve interesting problems that range from the lottery to diagnosing medical diseases. By teaching you basic principles and more advanced topics about theorems and models, this class will give you the tools to see the world in a different way that may not be intuitive but is proved by the math behind it.

Topics: open, high school, probability, random, lecture notes, bayes' rule, counting, discrete random...

Naval Postgraduate School

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697

Jan 25, 2013
01/13

by
Cox, Lyle Ashton.;Taylor, C. F.;Burnham, R.;Coulter, R.;Smart, S.

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SLED FORTRAN implementation / C.F. Taylor--SLED PASCAL implementation / R. Burnham, R. Coulter, and S. Smart.

Topics: RANDOM VARIABLES., PROBABILITIES., GAUSSIAN PROCESSES., TIME-SERIES ANALYSIS.

Journal of Research of the National Bureau of Standards

Topics: Accuracy, approximations, asymptotic expansion, Cauchy distribution, characteristic function,...

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363

May 31, 2011
05/11

by
NON

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The NASA Glenn Research Center (GRC) is developing and demonstrating communications and network technologies that are helping to enable the near-Earth space Internet. GRC envisions several service categories. The first of these categories is direct data distribution or D3 (pronounced ''D-cubed''). Commercially provided D3 will make it possible to download a data set from a spacecraft, like the International Space Station. as easily as one can extract a file from a remote server today, using a...

Topics: BOUNDARY CONDITIONS, VARIABILITY, BURGER EQUATION, MATHEMATICAL MODELS, UNCERTAIN SYSTEMS, ERROR...

Statistical Signal Processing, An Introduction to

Topics: random, probability, process, discrete, function, pdf, variable, space, variables, processes,...

327
327

Sep 20, 2010
09/10

by
Uphoff, Chaunce

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This paper is a presentation of some practical aspects of orbital transfer from Geosynchronous Transfer Orbit (GTO) to close, near-circular orbits of the Moon. The intent is to identify the important parameters affecting the problem and to bound (approximately) the range of required delta V for a spacecraft that has been placed in GTO. The basic geometric relationships are described and the dynamics are simulated by use of the Zero-Sphere-of Influence Patched Conic method. It is found that the...

Topics: ANALYSIS (MATHEMATICS), EXPONENTIAL FUNCTIONS, MATHEMATICAL MODELS, PETRI NETS, MARKOV CHAINS,...

Bell System Technical Journal, 52: 9. November 1973 pp 1483-1519. A Geometric Theory of Intersymbol Interference, Part I: Zero-Forcing and Decision-Feedback Equalization. (Messerschmitt, D.G.)

Topics: dfe, zfe, geometric, filter, linear, theory, random, intersymbol, orthogonal, finite, intersymbol...

"NPS-69-79-010"--Cover

Topics: RANDOM VARIABLES., TIME-SERIES ANALYSIS., PROBABILITIES.

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May 26, 2011
05/11

by
Ford, Kevin S

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Venus Flyer Robot (VFR) is an aerobot; an autonomous balloon probe designed for remote exploration of Earth's sister planet in 2003. VFR's simple navigation and control system permits travel to virtually any location on Venus, but it can survive for only a limited duration in the harsh Venusian environment. To help address this limitation, we develop: (1) a global circulation model that captures the most important characteristics of the Venusian atmosphere; (2) a simple aerobot model that...

Topics: AEROSPACE ENGINEERING, BAYES THEOREM, COMBINATORIAL ANALYSIS, QUALITY CONTROL, STATISTICS,...

Bell System Technical Journal, 41: 2. March 1962 pp 463-501. The One-Sided Barrier Problem for Gaussian Noise. (Slepian, David)

Topics: theorem, covariance, nonnegative, bounds, arcsin, covariances, random, gaussian, probability,...

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May 31, 2011
05/11

by
ODell, Keith P

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An automated inspection system has been developed to inspect the o-ring sealing surfaces on the Space Shuttle reusable solid rocket motor (RSRM) case segment joints. A laser digitizing system is used to create a three dimensional map of the o-ring sealing surfaces. This data is analyzed for any irregularities, which are noted for further inspection and disposition. This paper describes both the hardware and the software used to gather data as well as the methods developed to analyze the data....

Topics: COMPUTERIZED SIMULATION, PARACHUTES, TRAJECTORIES, MONTE CARLO METHOD, AEROMANEUVERING, MARS...

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279

Jun 1, 2011
06/11

by
Li, Wu; Padula, Sharon L

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The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of B-spline control points as design variables yet the resulting airfoil shape is fairly smooth, and (3) it allows the user to make a trade-off between the level of optimization and the amount of...

Topics: FLEXIBLE WINGS, RANDOM VARIABLES, FINITE DIFFERENCE THEORY, AIRCRAFT DESIGN, RELIABILITY ANALYSIS,...

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279

May 27, 2011
05/11

by
Majumdar, Alok; Schallhorn, Pau

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This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational...

Topics: DYNAMIC STRUCTURAL ANALYSIS, EIGENVECTORS, RANDOM VARIABLES, PROBABILITY DISTRIBUTION FUNCTIONS,...

"NPS-71-83-002."

Topics: Navigation, Naval tactics, Random variables, Estimation theory, Calculating machines

Bell System Technical Journal, 34: 6. November 1955 pp 1287-1315. Analysis of Switching Networks. (Lee, C.Y.)

Topics: probability, switching, blocking, network, retrial, random, networks, graph, path, link, switching...

Bell System Technical Journal, 60: 8. October 1981 pp 1927-1940. Numerical Integration of Stochastic Differential Equations - II. (Greenside, H.S.; Helfand, E. )

Topics: equations, parameters, stochastic, sdes, differential, deterministic, vector, algorithm,...

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May 29, 2011
05/11

by
Dennis, Henry J., Jr.; Sanders, Ti

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This presentation consists of viewgraph which review the test program and the results of the tests for the Gas Generator (GG) component for the Fastrac Engine. Included are pictures of the Fastrac (MC-1) Engine and the GG, diagrams of the flight configuration, and schematics of the LOX, and the RP-1 systems and the injector assembly. The normal operating parameters are reviewed, as are the test instrumentation. Also shown are graphs of the hot gas temperature, and the test temperature profiles....

Topics: RELIABILITY, RISK, PROCEDURES, FAILURE ANALYSIS, REDUNDANCY, SYSTEM FAILURES, FAILURE, MONTE CARLO...

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Jul 12, 2010
07/10

by
Liebert, J

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Numerous discoveries with the IUE Observatory have stimulated research on most spectroscopic types of degenerate dwarf stars. The hottest helium-rich cases apparently have substantial abundances of certain ions heavier than helium, due most likely to selective radiative acceleration. Hydrogen DA stars show trace abundances at temperatures as low as 20,000 K and provide evidence for modest outflowing winds. Cooler DA stars exhibit mysterious broad features near 1400A and 1600A. The element...

Topics: ADAPTIVE CONTROL, STOCHASTIC PROCESSES, DATA PROCESSING EQUIPMENT, MULTIVARIATE STATISTICAL...

Bell System Technical Journal, 58: 10. December 1979 pp 2289-2299. Numerical Integration of Stochastic Differential Equations. (Helfand, E.)

Topics: numerical, stochastic, equations, approximation, differential, parameters, random, gaussian,...

Bell System Technical Journal, 45: 3. March 1966 pp 359-395. The Capacity of the Band-Limited Gaussian Channel. (Wyner, A.D.)

Topics: channel, code, gaussian, capacity, noise, error, probability, theorem, model, decoding, product...

From the bitsavers.org collection, a scanned-in computer-related document. national :: appNotes :: AN-0255

Topics: spectral, random, density, function, equation, fourier, variance, probability, transform,...

Naval Postgraduate School

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241

Dec 12, 2012
12/12

by
Lawrance, A. J.Lewis, Peter Adrian Walter.

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"NPS-55-82-011"--Cover

Topics: Random variables, Exponential functions, Probabilities

Bell System Technical Journal, 39: 2. March 1960 pp 333-350. Amplitude Distribution of Shot Noise. (Gilbert, E.N.; Pollak, H.O.)

Topics: integral, amplitude, noise, equation, laplace, impulse, measure, distribution, noises, function,...

Bell System Technical Journal, 46: 9. November 1967 pp 2081-2089. A Normal Limit Theorem for Power Sums of Independent Random Variables. (Marlow, N.A.)

Topics: theorem, normal, random, log, variables, mutually, limit, power, lim, sums, mutually independent,...

Naval Postgraduate School

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Nov 30, 2012
11/12

by
Richbourg, Robert F.;Rowe, Neil C.;Zyda, Michael J.;McGhee, Robert (Robert B.)

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Title from cover

Topics: TIME-SERIES ANALYSIS., PROBABILITIES., RANDOM VARIABLES.

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Jan 18, 2012
01/12

by
Nassim Nicholas Taleb

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Topics: Investments., Chance., Random variables.

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214

Jul 11, 2010
07/10

by
Hess, R. V

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Atmospheric transmission of high energy CO2 lasers is considerably improved by high pressure operation which, due to pressure broadening, permits tuning the laser lines off atmospheric absorption lines. Pronounced improvement is shown for horizontal transmission at altitudes above several kilometers and for vertical transmission through the entire atmosphere. Applications of tunable high pressure CO2 lasers to energy transmission and to remote sensing are discussed along with initial efforts in...

Topics: MONTE CARLO METHOD, PARAMETERIZATION, PAYLOADS, STRUCTURAL DESIGN CRITERIA, DYNAMIC LOADS, DYNAMIC...

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213

Jul 11, 2010
07/10

by
Brundidge, K. C

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The structure of wakes and how this structure is related to the size and shape of buildings and other obstacles, and to ambient winds, was investigated. Mean values of natural atmospheric flow were obtained and used in conjunction with theoretical relationships developed by dimensional analysis to establish a model of the flow in the wake. Results indicate that conventional and V/STOL aircraft passing through the wake during takeoff and landing would experience not only a change in turbulence...

Topics: LINEAR TRANSFORMATIONS, OPTICAL DATA PROCESSING, ALGORITHMS, NORMAL DENSITY FUNCTIONS, RANDOM...

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Jun 12, 2011
06/11

by
Wilner, David J

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We summarize progress on our program to use high angular resolution imaging of thermal dust continuum emission at millimeter and submillimeter wavelengths to probe the structure of protoplanetary disks and debris disks around nearby stars.

Topics: IMAGING TECHNIQUES, DATA MINING, RANDOM VARIABLES, DATA STRUCTURES, DATA PROCESSING, VECTORS...

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Jul 5, 2010
07/10

by
Lambrecht, J

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No Abstract Available

Topics: MARKOV CHAINS, RANDOM VARIABLES, RANGE (EXTREMES), PROBABILITY THEORY, THEOREM PROVING

Bell System Technical Journal, 45: 6. July-August 1966 pp 979-984. Error Probabilities in Data System Pulse Regenerator with DC Restoration. (Zador, P.L.)

Topics: error, probability, random, probabilities, system, regenerator, filter, noise, input, sgn, binary...

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Jan 27, 2012
01/12

by
Rosenthal, Jeffrey S. (Jeffrey Seth)

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Includes index

Topics: Probability & Statistics - General, Mathematics, Probabilities, Random variables, Chance,...

Bell System Technical Journal, 53: 9. November 1974 pp 1681-1721. Source Coding for a Simple Network. (Gray, R.M.; Wyner, A.D.)

Topics: theorem, source, lemma, probability, channel, log, random, coding, code, defined, common channel,...

Bell System Technical Journal, 59: 3. March 1980 pp 367-415. On Prediction of Moving-Average Processes. (Shepp, L.A.; Slepian, D.; Wyner, A.D.)

Topics: estimator, random, prediction, entropy, density, bell, linear, processes, theorem, exponential,...

Bell System Technical Journal, 62: 10. December 1983 pp 2993-3006. On the Average Product of Gauss-Markov Variables. (Logan, B.F. Jr.; Mazo, J.E.; Odlyzko, A.M.; Shepp, L.A.)

Topics: bell, generating, variables, fraction, behavior, integral, define, continued, equation, sequence,...

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190

May 27, 2011
05/11

by
Turner, James E.; Hueter, Uw

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Currently, NASA and its industry partners are performing ground testing of hydrogen-fueled rocket based combined-cycle flowpaths. Successful ramjet and scramjet testing at Mach 6 and scramjet testing at Mach 8 have been performed. Cold flow mixing tests have also been successfully performed as have inlet operability tests. Additional testing of RBCC flowpaths at air augmented rocket and rocket only modes is underway.

Topics: RANDOM VARIABLES, SUBSTRUCTURES, DEGREES OF FREEDOM, MONTE CARLO METHOD, ALTERNATIVES, RELIABILITY,...

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May 23, 2011
05/11

by
Fox, Dennis S

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Silicon carbide fiber-reinforced silicon carbide (SiC/SiC) was exposed for 100 hours to dry, flowing oxygen. Oxidation kinetics were determined via thermogravimetric analysis at 981, 1204 and 1316 C (1800, 2200 and 2400 F). The effectiveness of three external coating systems applied for oxidation protection is discussed. In all cases, weight gains were observed, and the pyrolytic carbon interface layer remained intact. A CVD (Chemical Vapor Deposition) SiC external coating is the most promising...

Topics: STRUCTURAL DESIGN, CANTILEVER BEAMS, MEAN, STRUCTURAL FAILURE, SUBSTRUCTURES, FLEXIBILITY, DYNAMIC...

Bell System Technical Journal, 44: 3. March 1965 pp 401-426. Epoch Detection -- A Method for Resolving Overlapping Signals. (Young, Tzay Y.)

Topics: epoch, detection, overlapping, wavelet, max, wavelets, signals, signal, gaussian, hypothesis,...

Naval Postgraduate School

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175

Nov 30, 2012
11/12

by
Zyda, Michael J.;Taylor, Gary W.;McGhee, Robert (Robert B.)

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Title from cover

Topics: RANDOM VARIABLES., EXPONENTIAL FUNCTIONS., PROBABILITIES.

Bell System Technical Journal, 55: 7. September 1976 pp 875-903. Calculation of Multidisturber Crosstalk Probabilities - Application to Subscriber-Loop Gain. (Lapsa, P.M.)

Topics: crosstalk, probability, coupling, probabilities, distribution, intelligibility, random, noise,...

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May 31, 2011
05/11

by
Bradshaw, Jeffrey M.; Sierhuis, Maarten; Gawdiak, Yuri; Thomas, Hans; Greaves, Mark; Clancey, William J

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The Personal Satellite Assistant (PSA) is a softball-sized flying robot designed to operate autonomously onboard manned spacecraft in pressurized micro-gravity environments. We describe how the Brahms multi-agent modeling and simulation environment in conjunction with a KAoS agent teamwork approach can be used to support human-centered design for the PSA.

Topics: TRANSPORTATION NETWORKS, ROUTES, ALGORITHMS, SCHEDULES, RANDOM VARIABLES, STOCHASTIC PROCESSES,...

Current techniques for the prediction of ship motions in long-crested irregular waves are discussed. Format is provided for use of computer program SRIW which applies the method of linear superposition to regular-waves transfer functions obtained from experimental data or analytical predictions. Irregular wave spectra used are 323 point spectra measured at Station India in the North Atlantic and/or a series of mathematical spectra involving six parameters recently developed by Ochi.

Topics: DTIC Archive, Hubble, E. N., DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD...

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Jun 12, 2011
06/11

by
Vedantam, Nanda Kishor

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The objective of this study was to investigate the effects of the mean flow profiles on the instability characteristics in the near-injector region of low-density gas jets injected into high-density ambient gas mediums. To achieve this, a linear temporal stability analysis and a spatio-temporal stability analysis of a low-density round gas jet injected vertically upwards into a high-density ambient gas were performed by assuming three different sets of mean velocity and density profiles. The...

Topics: ROBUSTNESS (MATHEMATICS), COMPUTATIONAL FLUID DYNAMICS, UNCERTAIN SYSTEMS, SENSITIVITY, DERIVATION,...

Bell System Technical Journal, 55: 8. October 1976 pp 1125-1182. Distinguishing Stable Probability Measures - Part I: Discrete Time. (Stuck, B.W.)

Topics: probability, likelihood, characteristic, log, distributions, skewness, gaussian, stable, function,...

Bell System Technical Journal, 52: 10. December 1973 pp 1851-1865. A Universe Digital Data Scrambler. (Leeper, David G.)

Topics: scrambler, digital, sequence, source, universal, output, arbitrarily, binary, data, statistics,...