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2023 | Buch

Experiments, Sample Spaces, Events, and Probability Laws Kapitel lesen Erstes Kapitel lesen

Introduction to Probability and Random Variables

verfasst von: Orhan Gazi

Verlag: Springer Nature Switzerland

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This textbook provides a straightforward, clear explanation of probability and random variables for communications engineering students. The author focuses on the most essential subjects of probability and random variables, eliminating unnecessary details of this difficult subject. After an introduction to the topic, the author covers the essentials of experiments, sample spaces, events, and probability laws, while investigating how they relate to communications engineering work. He goes on to discuss total probability theorems, after which he covers discrete random variables and continuous random variables. The author uses his years of teaching probability and random variable concepts to engineering students to form the text in a very understandable manner. The book features exercises, examples, case studies, and other key classroom materials

Inhaltsverzeichnis

Frontmatter
Chapter 1. Experiments, Sample Spaces, Events, and Probability Laws
Abstract
In this chapter, we provide some fundamental definitions concerning the probability concept. First, we give information about experiments, sample spaces, and events and then introduce probability laws. Succeeding the explanation of probability laws, the concept of conditional probability is explained together with solved examples.
Orhan Gazi
Chapter 2. Total Probability Theorem, Independence, Combinatorial
Abstract
In Chap. 1, we explained fundamental definitions, such as experiment, sample space, event, probability, conditional probability, etc. In this chapter, we study the applications and uses of these definitions for real problems. The applications of fundamental definitions to real problems create some new concepts such as total probability theorem, Bayes’ rule, independent trials, counting principle, etc. We explain these new concepts with solved examples.
Orhan Gazi
Chapter 3. Discrete Random Variables
Abstract
Random variables are nothing but some mathematical functions used for some experiments, and these experiments can be both discrete and continuous. A random variable function is used to characterize an experiment. Once you define a random variable for an experiment, then you have full statistical knowledge of the random experiment. Today, we cannot consider a scientific research area that does not use the concept of random variables. Random variables can be considered one of the most important topics of mathematics that finds application in many engineering areas. Random variables can be classified as discrete and continuous random variables. We first study the discrete random variables due to their ease of understanding and then proceed with the continuous random variables.
Orhan Gazi
Chapter 4. Functions of Random Variables
Abstract
For the simple events of a sample space, we can define more than one random variable function; in fact, we can define infinitely many random variable functions, i.e., random variables, and for a variety number of random variables, we can define joint probability mass and cumulative distribution function. In this chapter, we provide information about joint probability mass functions of more than one random variable, functions of random variables, conditional probability mass functions, and corresponding mean and variance calculations. Solved examples are utilized to explain the subjects in a clear manner.
Orhan Gazi
Chapter 5. Continuous Random Variables
Abstract
In the previous chapters, we focused on the discrete experiments and for the discrete experiments we defined discrete sample spaces, events, and discrete random variables. Discrete sample spaces include a countable number of simple events. In this chapter, we study continuous experiments and define continuous sample spaces, continuous events, and continuous random variables. Continuous sample spaces include an uncountable number of simple events. For this reason, real number intervals are used to define the sample spaces and events for continuous experiments. Probability density function, cumulative distribution function, and mean and variance concepts for continuous random variables are explained by solved examples. Besides, conditional mean and variance calculations will be visited shortly.
Orhan Gazi
Chapter 6. More Than One Random Variables
Abstract
In this chapter, we consider joint statistical parameters of more than a single random variable. Starting from the joint distribution of two random variables, we provide information about the mean and variance calculation and marginal probability evaluation for jointly distributed random variables. In addition, we also consider the calculation of joint probability density function of two random variables using the joint probability density function of two other random variable pairs.
Orhan Gazi
Backmatter
Metadaten
Titel
Introduction to Probability and Random Variables
verfasst von
Orhan Gazi
Copyright-Jahr
2023
Electronic ISBN
978-3-031-31816-0
Print ISBN
978-3-031-31815-3
DOI
https://doi.org/10.1007/978-3-031-31816-0

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