Essentials of Mathematical Statistics

ISBN-10: 144968534X

ISBN-13: 9781449685348

Edition: 2014

Authors: Brian Albright
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Description: Part of the Jones and Bartlett Learning International Series in MathematicsWritten for the one-term introductory probability and statistics course for mid- to upper-level math and science majors, Essentials of Mathematical Statistics combines the topics generally found in main-stream elementary statistics books with the essentials of the underlying theory. The book begins with an axiomatic treatment of probability followed by chapters on discrete and continuous random variables and their associated distributions. It then introduces basic statistical concepts including summarizing data and interval parameter estimation, stressing the connection between probability and statistics. Final chapters introduce hypothesis testing, regression, and non-parametric techniques. All chapters provide a balance between conceptual understanding and theoretical understanding of the topics at hand. Key Features of Essentials of Mathematical Statistics:- End-of-section exercises range from computational to conceptual to theoretical.- Many sections include a sub-section titled “Software Calculations” which gives detailed descriptions of how to perform the calculations discussed in the section using the software Minitab, R, Excel, and the TI-83/84 calculators.- Provides a clear balance between conceptual understanding and theoretical understanding- Exercises throughout vary in level of difficulty and scope.

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Book details

List price: $244.95
Copyright year: 2014
Publisher: Jones & Bartlett Learning, LLC
Publication date: 2/19/2013
Binding: Hardcover
Pages: 598
Size: 7.75" wide x 9.50" long x 1.25" tall
Weight: 2.794
Language: English

Preface
Basics of Probability
Introduction
Basic Concepts and Definitions
Counting Problems
Axioms of Probability and the Addition Rule
Conditional Probability and the Multiplication Rule
Bayes' Theorem
Independent Events
Discrete Random Variables
Introduction
Probability Mass Functions
The Hypergeometric and Binomial Distributions
The Poisson Distribution
Mean and Variance
Functions of a Random Variable
The Moment-Generating Function
Continuous Random Variables
Introduction
Definitions
The Uniform and Exponential Distributions
The Normal Distribution
Functions of Continuous Random Variables
Joint Distributions
Functions of Independent Random Variables
The Central Limit Theorem
The Gamma and Related Distributions
Approximating the Binomial Distribution
Statistics
What Is Statistics?
Summarizing Data
Maximum Likelihood Estimates
Sampling Distributions
Confidence Intervals for a Proportion
Confidence Intervals for a Mean
Confidence Intervals for a Variance
Confidence Intervals for Differences
Sample Size
Assessing Normality
Hypothesis Testing
Introduction
Testing Claims About a Proportion
Testing Claims About a Mean
Comparing Two Proportions
Comparing Two Variances
Comparing Two Means
Goodness-of-Fit Tests
Test of Independence
One-Way ANOVA
Two-Way ANOVA
Simple Regression
Introduction
Covariance and Correlation
Method of Least Squares
The Simple Linear Model
Sums of Squares and ANOVA
Nonlinear Regression
Multiple Regression
Nonparametric Statistics
Introduction
The Sign Test
The Wilcoxon Signed-Rank Test
The Wilcoxon Rank-Sum Test
The Runs Test for Randomness
Proofs of Selected Theorems
A Proof of Theorem 3.7.5
A Proof of the Central Limit Theorem
A Proof of the Limit Theorem of De Moivre and Laplace
A Proof of Theorem 4.6.1
Confidence Intervals for the Difference of Two Means
Coefficients in the Linear Regression Equation
Wilcoxon Signed-Rank Test Distribution
Software Basics
Minitab
R
Excel
TI-83/84 Calculators
Tables
Answers to Selected Exercises
Index
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