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