| Description |
1 online resource (294 pages). |
|
text file |
| Series |
De Gruyter Textbook
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De Gruyter textbook.
|
| Contents |
Preface ; Contents ; 1 Mathematics revision ; 1.1 Basic notions of sets ; 1.2 Basic concepts of combinatorics ; 1.2.1 More about binomial coefficients ; 1.2.2 Specific permutations and a generalization ; 1.3 Some special functions ; 1.4 Integration of bi-dimensional functions. |
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2 Introduction to probability 2.1 Mathematical models ; 2.2 Further examples of random experiments ; 2.3 Assigning probabilities to events ; 2.4 Basic notions of probability ; 3 Finite sample spaces ; 3.1 Equally likely outcomes ; 3.2 Variants of a random experiment. |
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4 Conditional probability and independence 4.1 Conditional probability ; 4.2 Bayes' theorem ; 4.3 Independent events ; 5 One-dimensional random variables ; 5.1 The concept of a random variable ; 5.2 Discrete random variables ; 5.3 The binomial distribution and extensions. |
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5.4 Continuous random variables 5.5 Distribution function ; 6 Functions of random variables ; 6.1 Continuous random variables ; 6.2 Discrete random variables ; 7 Bi-dimensional random variables ; 7.1 Discrete random variables ; 7.2 Continuous random variables. |
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7.3 Marginal distributions and independent variables 7.4 Conditional distributions and distribution functions ; 7.5 Functions of a random variable ; 8 Characteristics of random variables ; 8.1 The expected value of a random variable ; 8.2 Expectation of a function of a random variable. |
| Note |
8.3 Properties of the expected value. |
| Bibliography |
Includes bibliographical references and index. |
| Summary |
This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences, in particular to readers who need or want to learn by self-study. The author is convinced that sophisticated examples are more useful for the student than a lengthy formalism treating the greatest possible generality. From the content:Mathematics revisionIntroduction to probabilityFinite sample spacesConditional probability and independenceOne-dimensional random variablesFunctions of random variablesBi-dimensional random variablesCharacteristics of random variablesDiscrete probability modelsContinuous probability modelsGenerating functions in probabilitySums of many random variablesSamples and sampling distributionsEstimation of parametersHypothesis tests. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Probabilities.
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Probabilities. |
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Mathematical statistics.
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Mathematical statistics. |
| Genre/Form |
Electronic books.
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| Other Form: |
Print version: Zörnig, Peter. Probability Theory and Statistical Applications : A Profound Treatise for Self-Study. Berlin/Boston : De Gruyter, ©2016 9783110363197 |
| ISBN |
9783110402711 (electronic book) |
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3110402718 (electronic book) |
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9783110402834 |
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3110402831 |
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9783110363197 |
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3110363194 |
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