Introduction to Statistics E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

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

Leseprobe

Simone Malacrida

Introduction to Statistics

BookRix GmbH & Co. KG81371 Munich

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

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INTRODUCTION

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I – COMBINATORY CALCULATION

Definitions

Operations

Applications

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II – ELEMENTARY STATISTICS

Chance

Conditional probability and Bayes' theorem

Elementary statistics

Applications

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III - ADVANCED STATISTICS

Introduction

Random variables, distributions and properties

Notable inequalities

Convergence

Discrete distributions

Continuous distributions

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IV - STATISTICAL INFERENCE

Introduction

Estimation theory

Hypothesis testing

Regression

Bayesian inference

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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

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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 positive integer as the multiplication of the first n positive integers less than or equal to that number.

The factorial symbol is given by an exclamation point following the number itself.

In formulas we have:

By definition 0!=1 and therefore the factorial operation is also computed recursively:

The binomial coefficient between two integers (positive and negative) is given by :

The properties of the binomial coefficient are given by: