Introduction to Mathematical Statistics and Its Applications

ISBN-10: 013487174X

ISBN-13: 9780134871745

Edition: 2nd 1986

List price: $105.00
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Book details

List price: $105.00
Edition: 2nd
Copyright year: 1986
Publisher: Prentice Hall PTR
Binding: Hardcover
Pages: 640
Size: 7.50" wide x 9.75" long x 1.25" tall
Weight: 2.332

Ph.D., Rutgers Univ

Ph.D., Tulane Univ

A Brief History
Some Examples
A Chapter Summary
Sample Spaces and the Algebra of Sets
The Probability Function
Discrete Probability Functions
Continuous Probability Functions
Conditional Probability
Repeated Independent Trials
Combinatorial Probability
Random Variables
The Probability Density Function
The Hypergeometric and Binomial Distributions
The Cumulative Distribution Function
Joint Densities
Independent Random Variables
Combining and Transforming Random Variables
Order Statistics
Conditional Densities
Expected Values
Properties of Expected Values
The Variance
Properties of Variances
Chebyshev's Inequality
Higher Moments
Moment-Generating Functions
Minitab Applications
Special Distributions
The Poisson Distribution
The Normal Distribution
The Geometric Distribution
The Negative Binomial Distribution
The Gamma Distribution
Minitab Applications
A Proof of the Central Limit Theorem
Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments
Interval Estimation
Properties of Estimators
Minimum-Variance Estimators: The Cramer-Rao Lower Bound
Minitab Applications
Hypothesis Testing
The Decision Rule
Testing Binomial Data-H0: p = p
Type I and Type II Errors
A Notion of Optimality: The Generalized Likelihood Ratio
The Normal Distribution
Point Estimates for �Ǡm and �Ǡs2
The �Ǡc2 Distribution
Inferences about �Ǡs2
The F and t Distributions
Drawing Inferences about �Ǡm
Minitab Applications
Some Distribution Results for Y and S
Appendix 7.A.3: A Proof of Theorem 7.3.5
A Proof That the One-Sample t
Test Is a GLRT
Types of Data: A Brief Overview
Classifying Data
Two-Sample Problems
Testing H 0: = The Two-Sample t Test
Testing H 0: = The F Test
Binomial Data: Testing H 0 px = py
Confidence Intervals for the Two-Sample Problem
A Derivation of the Two-Sample t
Test (A Proof of Theorem 9.2.2.)
Power Calculations for a Two-Sample t Test
Minitab Applications
Goodness-of-Fit Tests
The Multinomial Distribution
Goodness-of-Fit Tests: All Parameters Known
Goodness-of-Fit Tests: Parameters Unknown
Contingency Tables
Minitab Applications
The Method of Least Squares
The Linear Model
Covariance and Correlation
The Bivariate Normal Distribution
Minitab Applications
A Proof of Theorem 11.3.3
The Analysis of Variance
The F Test
Multiple Comparisons: Tukey's Method
Testing Subhypotheses with Orthogonal Contrasts
Data Transformations
Minitab Applications
A Proof of Theorem 12.2.2
The Distribution of $E{ down 12 SSTR/ up 12 (k-1)} over { down 12 SSE/ up 12 (n-k)}
When H1 Is True
Randomized Block Designs
The F Test for a Randomized Block Design
The Paired t Test
Minitab Applications
Nonparametric Statistics
The Sign Test
The Wilcoxon Signed Rank Test
The Kruskal-Wallis Test
The Friedman Test
Minitab Applications
Appendix: Statistical Tables
Answers to Selected Odd-Numbered Questions
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