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This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field. This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks and the Kalman-Bucy filter. Examples are discussed in detail, and there are a large number of exercises. This third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.
These notes describe how to average and fit numerical data that have been obtained either by simulation or measurement. Following an introduction on how to estimate various average values, they discuss how to determine error bars on those estimates, and how to proceed for combinations of measured values. Techniques for fitting data to a given set of models will be described in the second part of these notes. This primer equips readers to properly derive the results covered, presenting the content in a style suitable for a physics audience. It also includes scripts in python, perl and gnuplot for performing a number of tasks in data analysis and fitting, thereby providing readers with a useful reference guide.
Since the creation of the National Cooperative Educational Statistics System in 1988, states have joined with the National Center for Education Statistics to produce and maintain comparable and uniform education statistics. Through the National Forum on Education Statistics, states have met to develop and propose a set of basic data elements for voluntary use. Using these data elements will provide more comparable and reliable education information for any educational system adopting the common terminology. The basic data elements will not meet every education information purpose, but a set of basic data elements should help answer the most frequently asked questions about the administration, status, quality, operation, and performance of schools and school systems. This report presents a process for selecting and including new data elements in an information system and the student and staff elements that can be used to create information for conducting the day-to-day administration of schools and school districts; completing federal and state reports, and creating indicators that address questions about the success and functioning of education systems. The basic data elements selected for student information systems are grouped into categories of: (1) personal information; (2) enrollment; (3) school participation and activities; (4) assessment; (5) transportation; (6) health conditions, special program participation, and student support services; and (7) discipline. Similar elements defined for staff information systems include personal information, educational background, qualification information, current employment, assignments, and information on career development and separation from employment. An appendix contains discussions of policy questions, indicators, and basic data elements. (SLD)
This comprehensive text presents descriptive and inferential statistics with an assortment of business examples and real data, and an emphasis on decision-making. The accompanying CD-ROM presents Excel and Minitab tutorials as well as data files for all the exercises and exmaples presented.
This valuable addition to the literature offers readers a comprehensive overview of recent brain imaging research focused on reading, writing and mathematics—a research arena characterized by rapid advances that follow on the heels of fresh developments and techniques in brain imaging itself. With contributions from many of the lead scientists in this field, a number of whom have been responsible for key breakthroughs, the coverage deals with the commonalities of, as well as the differences between, brain activity related to the three core educational topics. At the same time, the volume addresses vital new information on both brain and behavior indicators of developmental problems, and points out the new directions being pursued using current advances in brain imaging technologies as well as research-based interventions. The book is also a tribute to a new Edmund, J Safra Brain center for the study of learning Disabilities at the University of Haifa-Israel.
With limited authority over state lawmaking, but ultimate responsibility for the performance of government, how effective are governors in moving their programs through the legislature? This book advances a new theory about what makes chief executives most successful and explores this theory through original data. Thad Kousser and Justin H. Phillips argue that negotiations over the budget, on the one hand, and policy bills on the other are driven by fundamentally different dynamics. They capture these dynamics in models informed by interviews with gubernatorial advisors, cabinet members, press secretaries and governors themselves. Through a series of novel empirical analyses and rich case studies, the authors demonstrate that governors can be powerful actors in the lawmaking process, but that what they're bargaining over – the budget or policy – shapes both how they play the game and how often they can win it.
In this IBM Redbooks publication we describe and demonstrate dimensional data modeling techniques and technology, specifically focused on business intelligence and data warehousing. It is to help the reader understand how to design, maintain, and use a dimensional model for data warehousing that can provide the data access and performance required for business intelligence. Business intelligence is comprised of a data warehousing infrastructure, and a query, analysis, and reporting environment. Here we focus on the data warehousing infrastructure. But only a specific element of it, the data model - which we consider the base building block of the data warehouse. Or, more precisely, the topic of data modeling and its impact on the business and business applications. The objective is not to provide a treatise on dimensional modeling techniques, but to focus at a more practical level. There is technical content for designing and maintaining such an environment, but also business content. For example, we use case studies to demonstrate how dimensional modeling can impact the business intelligence requirements for your business initiatives. In addition, we provide a detailed discussion on the query aspects of BI and data modeling. For example, we discuss query optimization and how you can determine performance of the data model prior to implementation. You need a solid base for your data warehousing infrastructure . . . . a solid data model.
Learn the art and science of predictive analytics — techniques that get results Predictive analytics is what translates big data into meaningful, usable business information. Written by a leading expert in the field, this guide examines the science of the underlying algorithms as well as the principles and best practices that govern the art of predictive analytics. It clearly explains the theory behind predictive analytics, teaches the methods, principles, and techniques for conducting predictive analytics projects, and offers tips and tricks that are essential for successful predictive modeling. Hands-on examples and case studies are included. The ability to successfully apply predictive analytics enables businesses to effectively interpret big data; essential for competition today This guide teaches not only the principles of predictive analytics, but also how to apply them to achieve real, pragmatic solutions Explains methods, principles, and techniques for conducting predictive analytics projects from start to finish Illustrates each technique with hands-on examples and includes as series of in-depth case studies that apply predictive analytics to common business scenarios A companion website provides all the data sets used to generate the examples as well as a free trial version of software Applied Predictive Analytics arms data and business analysts and business managers with the tools they need to interpret and capitalize on big data.