Probability and Statistics

1st Edition

with Integrated Software Routines

Authors:
eBook ISBN: 9780080480381
Published Date: 25th October 2005
Page Count: 712
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Description

Probability and Statistics is a calculus-based treatment of probability concurrent with and integrated with statistics.

Key Features

• Incorporates more than 1,000 engaging problems with answers
• Includes more than 300 solved examples
• Uses varied problem solving methods

Junior/senior undergraduates and beginning graduate students in mathematics, engineering, business, management and the arts.

1 INTRODUCTION TO PROBABILITY 1.0 Introduction 1.1 Interpretations of Probability Objectivists Classical (a priori) Empirical or Relative Frequency (a posteriori) Mathematical or Axiomatic 1.2 Sets Set Algebra 1.3 Probability Parlance 1.4 Probability Theorems 1.5 Conditional Probability and Independence 1.6 Bayes’s Rule 1.7 Counting the Ways Two Fundamental Principles of Counting (FPC) and the Pigeonhole Principle Tree Diagrams Permutations Combinations Match Problem Revisited 1.8 Summary Problems Miscellaneous Software Exercises Self Quiz 1A: Conditional Probability Self Quiz 1B: Poker Probability

2 RANDOM VARIABLES, MOMENTS, AND DISTRIBUTIONS 2.0 Introduction 2.1 Random Variables 2.2 Distributions 2.3 Moments Information Content (Entropy) Higher Moments 2.4 Standardized Random Variables 2.5 Jointly Distributed Random Variables Discrete Joint Density Functions 2.6 Independence of Jointly Distributed Random Variables 2.7 Covariance and Correlation 2.8 Conditional Densities Functions 2.9 Moment Generating Functions 2.10 Transformation of Variables Transformation of 2 or More Variables 2.11 Summary Problems Review Paradoxes Software Exercises Self Quiz 2: Moments

3 SPECIAL DISCRETE DISTRIBUTIONS 158 3.0 Introduction 3.1 Discrete Uniform 3.2 Bernoulli Distribution 3.3 Binomial Distribution 3.4 Multinomial Distribution 3.5 Hypergeometric Distribution 3.6 Geometric Distribution 3.7 Negative Binomial Distribution 3.8 Poisson Distribution 3.9 Summary Problems Review Software Exercises Self Quiz 3: Discrete Distributions

4 SPECIAL CONTINUOUS DISTRIBUTIONS 4.0 Introduction 4.1 Continuous Uniform Distribution 4.2 Gamma Function 4.3 Gamma Family (Exponential, Chi-Square, Gamma) 4.4 Exponential Distribution 4.5 Chi-Square Distribution 4.6 Normal Distribution 4.7 Student t Distribution 4.8 Beta Distribution 4.9 Weibull Distribution 4.10 F Distribution 4.11 Summary Problems Miscellaneous Review Software Exercises Self Quiz 4: Continuous Distributions

5 SAMPLING, DATA DISPLAYS, MEASURES OF CENTRAL TENDENCIES, MEASURES OF DISPERSION, AND SIMULATION 5.0 Introduction 5.1 Data Displays Boxplots Frequency Distributions and Histograms 5.2 Measures of Location Mean Median Mode Trimmed Mean Robustness 5.3 Measures of Dispersion Sample Variance and Standard Deviation Interquartile Range (IQR) Median Absolute Deviation from the Median (MAD) Outliers Coefficient of Variation Skewness Kurtosis 5.4 Joint Distribution of X and S2 5.5 Simulation of Random Variables Rejection Method 5.6 Using Monte Carlo for Integration 5.7 Order Statistics 5.8 Summary Problems Software Exercises Self Quiz 5: Sampling and Data Displays

6 POINT AND INTERVAL ESTIMATION 6.0 Introduction 6.1 Unbiased Estimators and Point Estimates Cramér-Rao Inequality 6.2 Methods of Finding Point Estimates Method of Moments Estimators (MME) Maximum Likelihood Estimators (MLE) 6.3 Interval Estimates (Confidence Intervals) Trade-Off: Sample Size Confidence Interval When s Is Not Known Confidence Interval for the Difference between Two Means (m1 - m2 ) Confidence Interval for s2 of a Normal Distribution Confidence Interval for a Proportion Confidence Interval for the Difference between Two Proportions Confidence Interval for the Paired T-Test Confidence Intervals for Ratio of Variances s2 2/s21 6.4 Prediction Intervals 6.5 Central Limit Theorem (Revisited) 6.6 Parametric Bootstrap Estimation 6.7 Summary Problems Confidence Intervals Miscellaneous Software Exercises Self Quiz 6: Estimation and Confidence Intervals

7 HYPOTHESIS TESTING 7.0 Introduction 7.1 Terminology in Statistical Tests of Hypotheses 7.2 Hypothesis Tests: Means P-value Directional Tests 7.3 Hypothesis Tests: Proportions Fisher-Irwin Test 7.4 Hypothesis Tests for Difference between Two Means: Small Samples (n £ 30) s2 Known n < 30; s2 Unknown 7.5 Hypothesis Test with Paired Samples Paired vs. Unpaired Statistically Significant vs. Practically Significant 7.6 Hypothesis Tests: Variances Hypothesis Tests for the Equality of Two Variances 7.7 Hypothesis Tests for Independence, Homogeneity, and Goodness of Fit R ¥ C Contingency Tables Test for Homogeneity and Independence Goodness of Fit Probability Plots 7.8 Summary Problems Miscellaneous Software Exercises Self Test 7: Hypothesis Testing

8 REGRESSION 8.0 Introduction 8.1 Review of Joint and Conditional Densities 8.2 Simple Linear Regression Least Squares Estimation Other Models of Simple Linear Regression 8.3 Distribution of Estimators with Inference on Parameters Distribution of RV E Distribution of RV Yi Distribution of RV B Inference on the Slope b Distribution of RV A Inference on the Intercept a Distribution of RV 8.4 Variation Coefficient of Determination 8.5 Residual Analysis Lack of Fit F-Test 8.6 Convertible Nonlinear Forms for Linear Regression 8.7 Polynomial Regression 8.8 Multiple Linear Regression Multiple Linear Regression with Matrices 8.9 Multiple Regression Techniques Forward Selection Backward Elimination Model Variables Selection Criteria Stepwise Regression 8.10 Correlation Analysis 8.11 Summary Problems Miscellaneous Software Exercises Self Test 8: Regression

9 ANALYSIS OF VARIANCE 9.0 Introduction 9.1 Single-Factor Analysis The Bartlett Test for Homogeneity of Variances 9.2 Two-Way ANOVA without Replication To Block or Not to Block 9.3 Two-Way ANOVA with Replication 9.4 Multiple Comparisons of Treatment Means Contrasts Contrast Confidence Intervals Least Significant Difference (LSD), Fisher LSD, and Scheffe Procedures Tukey Method Bonferroni Method Tukey Method vs. Bonferroni Method 9.5 ANOVA and Regression 9.6 Analysis of Means (ANOM) Graphical Analysis of Treament Means 9.7 Summary Problems Review Software Exercises Self Quiz 9: Analysis of Variance

10 NONPARAMETRIC STATISTICS 10.0 Introduction 10.1 The Sign Test 10.2 Nonparametric Bootstrap Estimation 10.3 The Sign Test for Paired Data Type II Beta Error for the Sign-Test 10.4 The Wilcoxon Signed-Rank Test 10.5 Wilcoxon-Mann-Whitney (WMW) Rank Test for Two Samples 10.6 Spearman Rank Order Correlation Coefficient 10.7 Kendall’s Rank Correlation Coefficient (t) 10.8 Nonparametric Tests for Regression 10.9 Nonparametric Tests for ANOVA Kruskal-Wallis Friedman Test 10.10 Runs Test 10.11 Randomization Tests 10.12 Summary Problems Software Exercises

Details

No. of pages:
712
Language:
English
Published:
25th October 2005
Imprint:
eBook ISBN:
9780080480381