Text probability by pitman published by springer isbn

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Text: Probability, by Pitman, published by Springer, ISBN: 9780387979748 Topics List: I. Discrete probability. 1.First principles: outcome spaces, basic counting techniques, and partitions. 2.Venn diagrams and the inclusion-exclusion principle. 3.Conditional probability and independence; decision trees and Bayes’ Theorem. 4.Discrete random variables; mass and generating functions; joint distributions. 5.Binomial, hypergeometric, geometric, negative binomial, and Poisson variables; applications and relationships. 6.Statistics on discrete variables. II. Continuous probability 7.First principles: density functions, calculation of probabilities and statistics. 8.Moments and moment-generating functions. 9.Common distributions and their applications; exponential, gamma, uniform, normal. 10.The central limit theorem and normal approximation to the binomial distribution. 11.Relationships between the exponential, gamma, and Poisson distributions. 12.Hazard rates and survival functions. 13.Cumulative distribution functions, percentiles, and change of variables. 14.Joint distribution of continuous variables; independence and marginal distributions; density of a function of two variables
Page 1 2017-2018 Math 4545 Mathematics 4545 Analysis Overview Autumn 4 credits Catalog Description: Topics in calculus and analysis. Prerequisites: Either C- or better in 2153, 2162.xx, 2173, 2182H, or 4182H; or credit for 254, 263.xx, 263.01H, 264H, or equivalent; -and-C- or better in Math 2568, 5520H, or equivalent. Exclusions: Entry to this course is restricted to graduate students in Statistics or Biostatistics who have permission from the Departments of Statistics or Biostatistics. Text: Introduction to Real Analysis, by William F. Trench, Edition1.03, published by Library of Congress Cataloging-in-Publication Data, ISBN: 0-13-045786-8 Topics List: 1.Limits and continuity of functions. 2.Derivative, mean value theorem, optimization. 3.Sequences and series, uniform convergence, power series, Taylor's theorem. 4.Riemann integral, substitution, bounded variation, limit properties, Rieman-Stieltjes integral. 5.Multivariable functions, directional derivatives, chain rule, Taylor's theorem. 6.Inverse and implicit function theorems, Lagrange multipliers, multiple integrals, Jacobians, differentiation under the integral sign.
Page 1 2017-2018 Math 4547 Mathematics 4547 Introductory Analysis I Autumn, Spring 3 credits Catalog Description: 4547-4548 involved advanced calculus covering: sequences, limits, continuity, differentiation, Riemann integral, sequences and series of functions, Taylor series, and improper integrals. Prerequisite: C- or better in 3345, or credit for 345. Text: Introduction to Real Analysis, 4thedition, by Bartle & Sherbert, published by Wiley, ISBN: 9780471433316 Topics List: 1.Sequences and their limits. 2.Bolzano-Weierstrass Theorem and Cauchy’s criterion. 3.Convergence and absolute convergence of series. Tests for convergence.

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