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Between Certainty and Uncertainty

Statistics and Probability in Five Units with Notes on Historical Origins and Illustrative Numerical Examples

  • Ludomir M. Laudański

Part of the Intelligent Systems Reference Library book series (ISRL, volume 31)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Ludomir M. Laudański
    Pages 1-2
  3. Ludomir M. Laudański
    Pages 3-4
  4. Ludomir M. Laudański
    Pages 5-5
  5. BOOK ONE THEORY

    1. Front Matter
      Pages 7-7
    2. Ludomir M. Laudański
      Pages 9-36
    3. Ludomir M. Laudański
      Pages 37-65
    4. Ludomir M. Laudański
      Pages 67-85
    5. Ludomir M. Laudański
      Pages 87-127
    6. Ludomir M. Laudański
      Pages 129-157
    7. Ludomir M. Laudański
      Pages 159-161
  6. BOOK TWO EXERCISES

    1. Front Matter
      Pages 163-163
    2. Ludomir M. Laudański
      Pages 165-187
    3. Ludomir M. Laudański
      Pages 189-215
    4. Ludomir M. Laudański
      Pages 217-243
    5. Ludomir M. Laudański
      Pages 245-274
    6. Ludomir M. Laudański
      Pages 275-302
    7. Ludomir M. Laudański
      Pages 303-303
  7. Back Matter
    Pages 0--1

About this book

Introduction

„Between Certainty & Uncertainty” is a one-of–a-kind short course on statistics for students, engineers  and researchers.  It is a fascinating introduction to statistics and probability with notes on historical origins and 80 illustrative numerical examples organized in the five units:

 

·         Chapter 1  Descriptive Statistics:  Compressing small samples, basic averages - mean and variance, their main properties including God’s proof; linear transformations and z-scored statistics .

 

·         Chapter 2 Grouped data: Udny Yule’s concept of qualitative and quantitative variables. Grouping these two kinds of data. Graphical tools. Combinatorial rules and qualitative variables.  Designing frequency histogram. Direct and coded evaluation of quantitative data. Significance of percentiles.

 

·         Chapter 3 Regression and correlation: Geometrical distance and equivalent distances in two orthogonal directions  as a prerequisite to the concept of two regression lines. Misleading in interpreting two regression lines. Derivation of the two regression lines. Was Hubble right? Houbolt’s cloud. What in fact measures the correlation coefficient?

 

·         Chapter 4 Binomial distribution: Middle ages origins of the binomials; figurate numbers  and combinatorial rules. Pascal’s Arithmetical Triangle.  Bernoulli’s or Poisson Trials? John Arbuthnot curing binomials.  How Newton taught S. Pepys probability. Jacob Bernoulli’s Weak Law of Large Numbers and others.

 

·         Chapter 5  Normal distribution and binomial heritage – Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace.  

 

Keywords

Average Binomial Distribution Correlation Normal Distribution Regression Statistics Variable Variance

Authors and affiliations

  • Ludomir M. Laudański
    • 1
  1. 1.Rzeszow Technical UniversityRzeszowPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-25697-4
  • Copyright Information Springer-Verlag GmbH Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-25696-7
  • Online ISBN 978-3-642-25697-4
  • Series Print ISSN 1868-4394
  • Series Online ISSN 1868-4408
  • Buy this book on publisher's site