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Introduction to probability and statistical inference / George G. Roussas.

By: Material type: TextTextPublication details: Amsterdam : Elsevier, c2015.Edition: 2nd edDescription: xiv, 606 p. : illustrations ; 25 cmISBN:
  • 9780128001141
Subject(s): DDC classification:
  • 519.2 23 R864
Contents:
1. Some motivating examples and some fundamental concepts -- 2. The concept of probability and some basic results -- 3. Numerical characteristics of a random variable, some special random variables -- 4. Joint and conditional P.D.F.'s, conditional expectation and variance, moment generating function, covariance and correlation coefficient -- 5. Independence of random variables and some applications -- 6. Transformation of random variables -- 7. Some modes of convergence of random variables, applications -- 8. An overview of statistical inference -- 9. Point estimation -- 10. Confidence intervals and confidence regions -- 11. Testing hypotheses -- 12. More about testing hypotheses -- 13. A simple linear regression model -- 14. Two models of analysis of variance -- 15. Some topics in nonparametric inference-- Index.
Summary: An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. * Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities* Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding* A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines* Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions* Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual.
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Includes index.

1. Some motivating examples and some fundamental concepts --
2. The concept of probability and some basic results --
3. Numerical characteristics of a random variable, some special random variables --
4. Joint and conditional P.D.F.'s, conditional expectation and variance, moment generating function, covariance and correlation coefficient --
5. Independence of random variables and some applications --
6. Transformation of random variables --
7. Some modes of convergence of random variables, applications --
8. An overview of statistical inference --
9. Point estimation --
10. Confidence intervals and confidence regions --
11. Testing hypotheses --
12. More about testing hypotheses --
13. A simple linear regression model --
14. Two models of analysis of variance --
15. Some topics in nonparametric inference--
Index.

An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. * Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities* Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding* A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines* Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions* Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual.

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