Table of Contents
Table of Contents
"Exercises of Combinatory Calculus"
INTRODUCTION
COMBINATORY CALCULATION
ELEMENTARY STATISTICS
"Exercises of Combinatory Calculus"
"Exercises of Combinatory Calculus"
SIMONE MALACRIDA
In this book, exercises are carried out regarding the following mathematical topics:
combinatorial calculus and calculus of probability
conditional probability and Bayes' theorem
calculation of statistical parameters: mean, median, mode and variance
Initial theoretical hints are also presented to make the performance of the exercises understood
Simone Malacrida (1977)
Engineer and writer, has worked on research, finance, energy policy and industrial plants.
ANALYTICAL INDEX
––––––––
INTRODUCTION
––––––––
I – COMBINATORY CALCULATION
Exercise 1
Exercise2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Exercise 19
Exercise 20
Exercise 21
Exercise 22
Exercise 23
––––––––
II – ELEMENTARY STATISTICS
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Exercise 19
Exercise 20
Exercise 21
INTRODUCTION
INTRODUCTION
In this workbook, some examples of calculations related to elementary statistics and combinatorics are carried out.
These topics are the necessary prerequisite for the study of advanced statistics and are of unavoidable importance.
In order to understand in more detail what is explained in the resolution of the exercises, the reference theoretical context is recalled at the beginning of each chapter.
What is presented in this workbook is generally addressed during the final three years of high school and, in a more detailed way, in university statistics courses.
I
COMBINATORY CALCULATION
COMBINATORY CALCULATION
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:
The penultimate property generalizes the construction of the binomial coefficients according to the Tartaglia triangle.
The last property is used instead to define the binomial theorem, also called Newton's formula or Newton's binomial or binomial expansion which expresses the expansion in the n-th power of any binomial:
––––––––
A simple permutation (or without repetitions) is an ordered sequence of the elements of a
Impressum
Verlag: BookRix GmbH & Co. KG
Tag der Veröffentlichung: 23.04.2023
ISBN: 978-3-7554-4001-7
Alle Rechte vorbehalten