Advances in computing technology – particularly in science and business – have increased the need for more statistical scientists to examine the huge amount of data being collected. Written by veteran statisticians, Probability and Statistical Inference, 10th Edition emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. This applied introduction to probability and statistics reinforces basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. It is designed for a two-semester course, but it can be adapted for a one-semester course. A good calculus background is needed, but no previous study of probability or statistics is required. Table of Contents 1. Probability 1.1 Properties of Probability 1.2 Methods of Enumeration 1.3 Conditional Probability 1.4 Independent Events 1.5 Bayes' Theorem 2. Discrete Distributions 2.1 Random Variables of the Discrete Type 2.2 Mathematical Expectation 2.3 Special Mathematical Expectations 2.4 The Binomial Distribution 2.5 The Hypergeometric Distribution 2.6 The Negative Binomial Distribution 2.7 The Poisson Distribution 3. Continuous Distributions 3.1 Random Variables of the Continuous Type 3.2 The Exponential, Gamma, and Chi-Square Distributions 3.3 The Normal Distribution 3.4 Additional Models 4. Bivariate Distributions 4.1 Bivariate Distributions of the Discrete Type 4.2 The Correlation Coefficient 4.3 Conditional Distributions 4.4 Bivariate Distributions of the Continuous Type 4.5 The Bivariate Normal Distribution 5. Distributions of Functions of Random Variables 5.1 Functions of One Random Variable 5.2 Transformations of Two Random Variables 5.3 Several Independent Random Variables 5.4 The Moment-Generating Function Technique 5.5 Random Functions Associated with Normal Distributions 5.6 The Central Limit Theorem 5.7 Approximations for Discrete Distributions 5.8 Chebyshev's Inequality and Convergence in Probability 5.9 Limiting Moment-Generating Functions 6. Point Estimation 6.1 Descriptive Statistics 6.2 Exploratory Data Analysis 6.3 Order Statistics 6.4 Maximum Likelihood and Method of Moments Estimation 6.5 A Simple Regression Problem 6.6 Asymptotic Distributions of Maximum Likelihood Estimators 6.7 Sufficient Statistics 6.8 Bayesian Estimation 7. Interval Estimation 7.1 Confidence Intervals for Means 7.2 Confidence Intervals for the Difference of Two Means 7.3 Confidence Intervals for Proportions 7.4 Sample Size 7.5 Distribution-Free Confidence Intervals for Percentiles 7.6 More Regression 7.7 Resampling Methods 8. Tests of Statistical Hypotheses 8.1 Tests About One Mean 8.2 Tests of the Equality of Two Means 8.3 Tests for Variances 8.4 Tests About Proportions 8.5 Some Distribution-Free Tests 8.6 Power of a Statistical Test 8.7 Best Critical Regions 8.8 Likelihood Ratio Tests 9. More Tests 9.1 Chi-Square Goodness-of-Fit Tests 9.2 Contingency Tables 9.3 One-Factor Analysis of Variance 9.4 Two-Way Analysis of Variance 9.5 General Factorial and 2k Factorial Designs 9.6 Tests Concerning Regression and Correlation 9.7 Statistical Quality Control APPENDICES A. References B. Tables C. Answers to Odd-Numbered Exercises D. Review of Selected Mathematical Techniques D.1 Algebra of Sets D.2 Mathematical Tools for the Hypergeometric Distribution D.3 Limits D.4 Infinite Series D.5 Integration D.6 Multivariate Calculus Index
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Mathematical statistics Probabilities Discrete Distributions Bivariate Distributions Point Estimation Interval Estimation Tests of Statistical Hypotheses