Mathematical Statistics with Applications

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  • Edition: 7th
  • Format: Hardcover
  • Copyright: 2007-10-10
  • Publisher: Cengage Learning
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In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.

Table of Contents

What Is Statistics? Introduction
Characterizing a Set of Measurements: Graphical Methods
Characterizing a Set of Measurements: Numerical Methods
How Inferences Are Made
Theory and Reality
Probability and Inference
A Review of Set Notation
A Probabilistic Model for an Experiment: The Discrete Case
Calculating the Probability of an Event: The Sample-Point Method
Tools for Counting Sample Points
Conditional Probability and the Independence of Events
Two Laws of Probability
Calculating the Probability of an Event: The Event-Composition Methods
The Law of Total Probability and Bayes's Rule
Numerical Events and Random Variables
Random Sampling
Discrete Random Variables and Their Probability Distributions
Basic Definition
The Probability Distribution for Discrete Random Variable
The Expected Value of Random Variable or a Function of Random Variable
The Binomial Probability Distribution
The Geometric Probability Distribution
The Negative Binomial Probability Distribution (Optional)
The Hypergeometric Probability Distribution
Moments and Moment-Generating Functions
Probability-Generating Functions (Optional)
Tchebysheff's Theorem
Continuous Random Variables and Their Probability Distributions
The Probability Distribution for Continuous Random Variable
The Expected Value for Continuous Random Variable
The Uniform Probability Distribution
The Normal Probability Distribution
The Gamma Probability Distribution
The Beta Probability Distribution
Some General Comments
Other Expected Values
Tchebysheff's Theorem
Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional)
Multivariate Probability Distributions
Bivariate and Multivariate Probability Distributions
Independent Random Variables
The Expected Value of a Function of Random Variables
Special Theorems
The Covariance of Two Random Variables
The Expected Value and Variance of Linear Functions of Random Variables
The Multinomial Probability Distribution
The Bivariate Normal Distribution (Optional)
Conditional Expectations
Functions of Random Variables
Finding the Probability Distribution of a Function of Random Variables
The Method of Distribution Functions
The Methods of Transformations
Multivariable Transformations Using Jacobians
Order Statistics
Sampling Distributions and the Central Limit Theorem
Sampling Distributions Related to the Normal Distribution
The Central Limit Theorem
A Proof of the Central Limit Theorem (Optional)
The Normal Approximation to the Binomial Distributions
The Bias and Mean Square Error of Point Estimators
Some Common Unbiased Point Estimators
Evaluating the Goodness of Point Estimator
Confidence Intervals
Large-Sample Confidence Intervals Selecting the Sample Size
Small-Sample Confidence Intervals for u and u1-u2
Confidence Intervals for o2
Properties of Point Estimators and Methods of Estimation
Relative Efficiency
The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation
The Method of Moments
The Method of Maximum Likelihood
Some Large-Sample Properties of MLEs (Optional)
Hypothesis Testing
Elements of a Statistical Test
Common Large-Sample Tests
Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test
Relationships Between Hypothesis Testing Procedures and Confidence Intervals
Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values
Some Comments on the Theory of Hypothesis Testing
Small-Sample Hypothesis Testing for u and u1-u2
Testing Hypotheses Concerning Variances
Power of Test and the Neyman-Pearson Lemma
Likelihood Ration Test
Linear Models and Estimation by Least Sq
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