Probability And Statistics Gtu

This book is designed for the 3rd semester gtu engineering students pursuing the probability and statistics (code 3130006). The crisp but complete explanation of topics will help the students easily understand the basic concepts. The tutorial approach (I.E. Teach by example) followed in the text will enable students develop a logical perspective to solving problems.

First chapter deals with probability and random variable discussion. CDF, PDF and two dimensional random variables are discussed. Second chapter presents various useful probability distribution models. It also presents useful statistical averages such as mean, moments, variance, etc. Third chapter presents basic statistics concepts. Mean, median, mode, moments, variance, Kurtosis, skewness are discussed. Correlation, regression, Chebyshev inequality are also presented. Fourth chapter discusses formation of hypothesis, tests of significance and chi-square distribution. Last chapter presents curve fitting using straight line and second degree parabola.

This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the benefit of the students

This book has been designed specifically for the Gujarat Technological University (GTU) syllabus and students of engineering in their Third Semester. Seven dedicated chapters are set to sequentially cover each module of the syllabus and are compounded by the ';tutorial technique', i.e., theory followed by example(s) so that the learner develops an increased sense of conscious intellection. This exceptional mix of theory and application caters to all types of requirements, be it the student or the teacher. Not only is the syllabus rigorously followed, but each topic has also been treated with the end-examination in sight. Concepts are well-aided with solved examples (of different complexities) so that every learner understands the topic at hand.

The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.

This open access book provides a comprehensive overview of the core subjects comprising mathematical curricula for engineering studies in five European countries and identifies differences between two strong traditions of teaching mathematics to engineers. The collective work of experts from a dozen universities critically examines various aspects of higher mathematical education. The two EU Tempus-IV projects – MetaMath and MathGeAr – investigate the current methodologies of mathematics education for technical and engineering disciplines. The projects aim to improve the existing mathematics curricula in Russian, Georgian and Armenian universities by introducing modern technology-enhanced learning (TEL) methods and tools, as well as by shifting the focus of engineering mathematics education from a purely theoretical tradition to a more applied paradigm. MetaMath and MathGeAr have brought together mathematics educators, TEL specialists and experts in education quality assurance form 21 organizations across six countries. The results of a comprehensive comparative analysis of the entire spectrum of mathematics courses in the EU, Russia, Georgia and Armenia has been conducted, have allowed the consortium to pinpoint and introduce several modifications to their curricula while preserving the generally strong state of university mathematics education in these countriesThe book presents the methodology, procedure and results of this analysis. This book is a valuable resource for teachers, especially those teaching mathematics, and curriculum planners for engineers, as well as for a general audience interested in scientific and technical higher education.

Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.

Visualizing the data is an essential part of any data analysis. Modern computing developments have led to big improvements in graphic capabilities and there are many new possibilities for data displays. This book gives an overview of modern data visualization methods, both in theory and practice. It details modern graphical tools such as mosaic plots, parallel coordinate plots, and linked views. Coverage also examines graphical methodology for particular areas of statistics, for example Bayesian analysis, genomic data and cluster analysis, as well software for graphics.