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"This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson Inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties."

"ABSTRAKDalam analisis multivariate klasik dalam suatu uji hipotesa sering digunakananalisis nilai eigen dalam penetuan statistik ujinya. Dibawah kondisi H0, nilaistatistik uji yang diperoleh akan digunakan untuk bentuk distribusi yang berkaitandengan statistik uji. Daerah kritis penolakan suatu uji uji hipotesa ditentukanberdasarkan bentuk distribusi yang diperoleh. Nilai eigen yang diperoleh untukanalisi multivariat ini untuk pembentukan statistik ujinya bisa menggunakanfungsi yang melibatkan keseluruhan nilai eigen atau dengan menggunakan nilaiyang ekstrem. Untuk nilai eigen yang maksimum statistik uji yang digunakanberdasar Roy test maksimum. Cara lain yang digunakan adalah denganpendekatan distribusi Tracy-Widom. Disamping daerah kritis yang diperoleh jugadibutuhkan p-value berdasar nilai statistik uji yang sebenarnya.

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"Introduction to probability, is written for upper-level undergraduate students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences. With his trademark clarity and economy of language, the author explains important concepts of probability, while providing useful exercises and examples of real world applications for students to consider. After introducing fundamental probability concepts, the book proceeds to topics including special distributions, the joint probability density function, covariance and correlation coefficients of two random variables, and more."

"In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers. The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers; solving linear recurrence relations; graph theory; Lucas numbers; and alternate Fibonacci numbers. The second half of the book explores Catalan numbers, and the author builds a complete foundation to the topic using a historical background and introductory examples, along with coverage of partial orders, total orders, topological sorting, graph theory, rooted ordered binary trees, pattern avoidance, and the Narayana numbers. Coverage of both topics are accompanied by interesting, real-world examples from areas such as sports, botany, and computer science. Each section concludes with detailed exercise sets that can also serve as extended examples of the presented material along with selected solutions. An Instructor’s Manual featuring complete solutions is available upon written request, and extensive reference sections outline resources for further study of the discussed topics."