Introduction to Statistics
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About this ebook
All mathematical topics related to statistics are presented in this book:
combinatorial calculus
probability and elementary statistics
random variables
continuous and discrete probability distributions
estimation theory and hypothesis testing
regression and Bayesian inference
stochastic processes
Simone Malacrida
Simone Malacrida (1977) Ha lavorato nel settore della ricerca (ottica e nanotecnologie) e, in seguito, in quello industriale-impiantistico, in particolare nel Power, nell'Oil&Gas e nelle infrastrutture. E' interessato a problematiche finanziarie ed energetiche. Ha pubblicato un primo ciclo di 21 libri principali (10 divulgativi e didattici e 11 romanzi) + 91 manuali didattici derivati. Un secondo ciclo, sempre di 21 libri, è in corso di elaborazione e sviluppo.
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Introduction to Statistics - Simone Malacrida
Table of Contents
Table of Contents
Introduction to Statistics
INTRODUCTION
COMBINATORY CALCULATION
ELEMENTARY STATISTICS
ADVANCED STATISTICS
STATISTICAL INFERENCE
STOCHASTIC PROCESSES
Introduction to Statistics
Introduction to Statistics
SIMONE MALACRIDA
All mathematical topics related to statistics are presented in this book:
combinatorial calculus
probability and elementary statistics
random variables
continuous and discrete probability distributions
estimation theory and hypothesis testing
regression and Bayesian inference
stochastic processes
Simone Malacrida (1977)
Engineer and writer, has worked on research, finance, energy policy and industrial plants.
ANALYTICAL INDEX
––––––––
INTRODUCTION
––––––––
I – COMBINATORY CALCULATION
Definitions
Operations
Applications
––––––––
II – ELEMENTARY STATISTICS
Chance
Conditional probability and Bayes' theorem
Elementary statistics
Applications
––––––––
III - ADVANCED STATISTICS
Introduction
Random variables, distributions and properties
Notable inequalities
Convergence
Discrete distributions
Continuous distributions
––––––––
IV - STATISTICAL INFERENCE
Introduction
Estimation theory
Hypothesis testing
Regression
Bayesian inference
––––––––
V - STOCHASTIC PROCESSES
Definitions
Markov chains and other processes
INTRODUCTION
INTRODUCTION
Statistics is now characterized as a discipline in its own right with respect to mathematics, even though its foundations are in the latter.
The expansion of statistical applications is now evident to everyone: statistical concepts are present in every scientific and technological field, in economics and politics, in sociology and in the human sciences.
The first two chapters of this book summarize the basic concepts, already understandable at the high school level.
Combinatorial calculus and the concept of probability are the first fundamentals of statistics.
Subsequently, the great leap forward given by the definitions of random variables and their distributions or laws of probability is presented.
Through the study of these distributions it is possible to study the characteristics of many relevant aspects at the application level.
Estimation theory, statistical inference and hypothesis testing are the main fields in which statistics play a predominant role.
Finally, we must not forget the statistical processes, i.e. those models that can be taken as a reference to compare practical cases.
It goes without saying that such knowledge requires in-depth mathematical preparation at university level.
I
COMBINATORY CALCULATION
COMBINATORY CALCULATION
Definitions
––––––––
Combinatorial calculus is the branch of mathematics that studies the possible configurations for grouping the elements of a finite set.
To do this it is necessary to introduce some operations that we are now going to expose.
We define the factorial operation of any