Probability and Statistical Inference, 7/e (精裝)

Robert V Hogg, Elliot A. Tanis

  • 出版商: Prentice Hall
  • 出版日期: 2005-01-30
  • 售價: $988
  • 語言: 英文
  • 頁數: 752
  • 裝訂: Hardcover
  • ISBN: 0131464132
  • ISBN-13: 9780131464131
  • 無法訂購

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Description:

This applied introduction to the mathematics of probability and statistics e mphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variability. Designed for students with a background in calculus, it reinforces basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts.

 

Table of Contents:

Chapter 1: Probability

Basic Concepts

Properties of Probability

Methods of Enumeration

Conditional Probability

Independent Events

Bayes' Theorem

Chapter 2: Discrete Distributions

Random Variables of the Discrete Type

Mathematical Expectation

Bernoulli Trials and the Binomial Distribution

The Moment-Generating Function

The Poisson Distribution

Chapter 3: Continuous Distributions

Continuous-Type Data and EDA

Random Variables of the Continuous Type

The Uniform and Exponential Distributions

The Gamma and Chi-Square Distributions

Distributions of Functions of a Random Variable

Additional Models

Chapter 4: Multivariate Distributions

Distributions of Two Random Variables

The Correlation Coefficient

Conditional Distributions

Transformations of Random Variables

Independent Random Variables

Distributions of Sums of Independent Random Variables

Chebyshev's Inequality and Convergence in Probability

Chapter 5: The Normal Distribution

A Brief History of Probability

The Normal Distribution

Random Functions Associated with Normal Distributions

The Central Limit Theorem

Approximations for Discrete Distributions

The Bivariate Normal Distribution

Limiting Moment-Generating Functions

Importance of Understanding Variability

Chapter 6: Estimation

Sample Characteristics

Point Estimation

Sufficient Statistics

Confidence Intervals for Means

Confidence Intervals for Difference of Two Means

Confidence Intervals for Variances

Confidence Intervals for Proportions

Sample Size

Order Statistics

Distribution-Free Confidence Intervals for Percentiles

A Simple Regression Problem

More Regression

Resampling Methods

Asymptotic Distributions of Maximum Likelihood Estimators

Chapter 7: Bayesian Methods

Subjective Probability

Bayesian Estimation

More Bayesian Concepts

Chapter 8: Tests of Statistical Hypotheses

Tests About Proportions

Tests About One Mean and One Variance

Tests of the Equality of Two Normal Distributions

The Wilcoxon Tests

Chi-Square Goodness of Fit Tests

Contingency Tables

One-Factor Analysis of Variance

Two-Factor Analysis of Variance

Tests Concerning Regression and Correlation

Kolmogorov-Smirnov Goodness of Fit Test

Run Test and Test for Randomness

Chapter 9: Theory of Statistical Inference

Power of a Statistical Test

Best Critical Regions

Likelihood Ratio Tests

Chapter 10: Quality Improvement Through Statistical Methods

Time Sequences

Statistical Quality Control

General Factorial and 2 k Factorial Designs

More on Design of Experiments

Epilogue

A Review of Selected Mathematical Techniques

Algebra of Sets

Mathematical Tools for the Hypergeometric Distribution

Limits

Infinite Series

Integration

Multivariate Calculus