A Modern Introduction to Probability and Statistics Understanding Why and How /

• Main Authors: Dekking, Frederik Michel (Author), Kraaikamp, Cornelis (Author), Lopuhaä, Hendrik Paul (Author), Meester, Ludolf Erwin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2005.
• Series: Springer Texts in Statistics,
• Subjects: Mathematics.; Probabilities.; Statistics.; Applied mathematics.; Engineering mathematics.; Probability Theory and Stochastic Processes.; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.; Appl.Mathematics/Computational Methods of Engineering.

Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is tha...

Table of Contents:

• Why probability and statistics?
• Outcomes, events, and probability
• Conditional probability and independence
• Discrete random variables
• Continuous random variables
• Simulation
• Expectation and variance
• Computations with random variables
• Joint distributions and independence
• Covariance and correlation
• More computations with more random variables
• The Poisson process
• The law of large numbers
• The central limit theorem
• Exploratory data analysis: graphical summaries
• Exploratory data analysis: numerical summaries
• Basic statistical models
• The bootstrap
• Unbiased estimators
• Efficiency and mean squared error
• Maximum likelihood
• The method of least squares
• Confidence intervals for the mean
• More on confidence intervals
• Testing hypotheses: essentials
• Testing hypotheses: elaboration
• The t-test
• Comparing two samples.