Computations with random variables

In this book you will find the basics of probability theory and statistics. In addition, there are several topics that go somewhat beyond the basics but that ought to be present in an introductory course: simulation, the Poisson process, the law of large numbers, and the central limit theorem. Computers have brought many changes in statistics. In particular, the bootstrap has earned its place. It provides the possibility to derive confidence intervals and perform tests of hypotheses where traditional (normal approximation or large sample) methods are inappropriate.

484p zizaybay1103 29-05-2024 3 1   Download

Probability and Computer science - Lecture 1: Introduction to probability. This lecture provides students with content including: mathematical tools to deal with uncertain events; applications include; combinatorial analysis; counting; axioms of probability; conditional probability and inference;... Please refer to the detailed content of the lecture!

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Probability and Computer science - Lecture 3: Basic probability - axioms, conditional probability, random variables, distributions. This lecture provides students with content including: application verifying polynomial identities; axioms of probability; analysis of the considered algorithm; notion of independence; notion of conditional probability; random variables; linearity of expectation;... Please refer to the detailed content of the lecture!

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Probability and Computer science - Lecture 7: Continuous distributions and poisson process. This lecture provides students with content including: continuous random variables; poisson process; queuing theory just a glance; uniform distribution; exponential distribution;... Please refer to the detailed content of the lecture!

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Continued part 1, part 2 of ebook "Fundamentals of digital communication" provides readers with contents including: Chapter 6 - Information-theoretic limits and their computation; Chapter 7 - Channel coding; Chapter 8 - Wireless communication; Appendix A - Probability, random variables, and random processes; Appendix B - The Chernoff bound;...

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Part 1 of ebook "Reliability-based design in geotechnical engineering: Computations and applications" provides readers with content including: numerical recipes for reliability analysis – a primer; spatial variability and geotechnical reliability; practical reliability approach using spreadsheet; Monte Carlo simulation in reliability analysis; practical application of reliability-based design in decision-making; randomly heterogeneous soils under static and dynamic loads;...

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Ebook A modern introduction to probability and statistics: Understanding why and how - Part 1 presents the following content: Chapter 1 why probability and statistics? chapter 2 outcomes, events, and probability, chapter 3 conditional probability and independence, chapter 4 discrete random variables, chapter 5 continuous random variables, chapter 6 simulation, chapter 7 expectation and variance, chapter 8 computations with random variables, chapter 9 joint distributions and independence, chapter 10 covariance and correlation, chapter 11 more computations with more random variables, chapter ...

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Many stochastic processes in practice having the sequences of random variables are generally skewed and dependent and to solve these problems, the application of first-order gamma autoregressive (GAR(1)) model[4] is very effective; especially in the study of streamflow simulation in Stochastic Hydrology. This paper mainly presents the study of Gar(1) model in the simulation of monthly streamflows. To reach this aim, we study Thomas-Fiering model and proposed the Gar(1)-Fragments model.

6p vikoenigsegg 29-09-2022 11 2   Download

The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the q-stripe TSP with q ≥ 1, the objective function sums the costs for traveling from one vertex to each of the next q vertices along the tour. To solve medium to large-sized instances, a metaheuristic approach is proposed. The proposed method has two main components, which are construction and improvement phases. The construction phase generates an initial solution using the Greedy Randomized Adaptive Search Procedure (GRASP).

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In this paper, an improved version of Differential Evolution algorithm, called iDE, is introduced to solve design optimization problems of composite laminated beams. The beams used in this research are Timoshenko beam models computed based on analytical formula. The iDE is formed by modifying the mutation and the selection step of the original algorithm. Particularly, individuals involved in mutation were chosen by Roulette wheel selection via acceptant stochastic instead of the random selection.

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Accumulated evidence shows that the abnormal regulation of long non-coding RNA (lncRNA) is associated with various human diseases. Accurately identifying disease-associated lncRNAs is helpful to study the mechanism of lncRNAs in diseases and explore new therapies of diseases.

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In general, the fluctuation of the elastic modulus of materials is crucial in structural analysis. This paper develops a stochastic finite element method (SFEM) for analyzing a nonuniform column considering the random process in elastic modulus. This random process of elastic modulus is assumed as a one-dimensional Gaussian random field. The weighted integration method is used to discretize the random field and establish the stochastic finite element formulation to compute the first and second moments of displacement fields.

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The linear mixed effect model allows considerable flexibility in the specification of the random effects structure but restricts the within group errors to be independent, identically distributed random variables with mean zero and constant variance. In this paper the linear mixed-effects model is extended to include heteroscedastic errors. In this paper several classes of variance functions to characterize heteroscedasticity are introduced. We describe how the lme() function can be used to fit the extended linear mixed effects model and illustrate its various capabilities through examples.

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The paper highlights cost and returns of coffee growing by tribal farmers at Paderu division in Visakhapatnam district of Andhra Pradesh.Data collection was done using pre tested questionnaire administrated on 90 coffee producers selected randomly. According to the study small scale traditional farms had negligible fixed costs. So we have not taken the fixed costs in computation of cost of cultivation of coffee in the present study. The gross margin analysis indicates average total variable cost of coffee was Rs.

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The present investigation was carried out in 49 groundnut genotypes to assess the nature and extent of genetic variability, heritability and genetic advance under normal (0 % polyethylene glycol-6000 as control) and osmotic stress condition (15 % polyethylene glycol-6000) in germination phases in three replications in a completely randomized design. The observations on germination per cent, root length, shoot length, fresh weight of seedlings and total dry matter were recorded on tenth day after incubation.

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The study was conducted in Andhra Pradesh state during 2017-18. A total of 120 Bt cotton tenant farmers were selected randomly for the study. Data was collected with interview schedule. To study the nature of the relationship between the profile characteristics and knowledge level of Bt cotton tenant farmers, correlation coefficients (r) was computed and the values were presented in Table 1. The relationship between the profile and knowledge level of Bt cotton tenant farmers were tested by null hypothesis and empirical hypothesis.

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This paper discusses predicting attendance at Major League Soccer events using data from the 2014 and 2015 seasons. Panel data is obtained for each team, season, and weather category. A traditional least squared dummy variable linear regression technique is used along with three machine learning algorithms – random forest, M5 prime, and extreme gradient boosting. Extreme gradient boosting provides superior results with respect to out-of-sample root mean square error statistics.

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In our work, we propose a metaheuristic algorithm which is mainly based on the principles of Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Descent (VND) to solve the problem. The GRASP is used to build an initial solution which is good enough in a construction phase.

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This is the standard textbook for courses on probability and statistics, not substantially updated. While helping students to develop their problem-solving skills, the author motivates students with practical applications from various areas of ECE that demonstrate the relevance of probability theory to engineering practice. Included are chapter overviews, summaries, checklists of important terms, annotated references, and a wide selection of fully worked-out real-world examples.

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With the ever increasing amounts of data in electronic form, the need for automated methods for data analysis continues to grow. The goal of machine learning is to develop methods that can automatically detect patterns in data, and then to use the uncovered patterns to predict future data or other outcomes of interest. Machine learning is thus closely related to the fields of statistics and data mining, but differs slightly in terms of its emphasis and terminology.

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