Probability: The Science of Uncertainty- with Applications to Investments, Insurance, and Engineering

By: Bean,Michael AMaterial type: TextTextSeries: Brooks/Cole series in advanced mathmaticsPublication details: Australia ; Pacific Grove, CA : Brooks/Cole, ©2001Description: xiii, 448 pages : illustrationsISBN: 9780534366032; 0534366031 Subject(s): ProbabilitiesDDC classification: 519.2
Contents:
What Is Probability? -- How Is Uncertainty Quantified? -- Probability in Engineering and the Sciences -- What Is Actuarial Science? -- What Is Financial Engineering? -- Interpretations of Probability -- Probability Modeling in Practice -- Outline of This Book -- A Survey of Some Basic Concepts Through Examples -- Payoff in a Simple Game -- Choosing Between Payoffs -- Future Lifetimes -- Simple and Compound Growth -- Classical Probability -- The Formal Language of Classical Probability -- Conditional Probability -- The Law of Total Probability -- Bayes' Theorem -- Appendix on Sets, Combinatorics, and Basic Probability Rules -- Random Variables and Probability Distributions -- Definitions and Basic Properties -- What Is a Random Variable? -- What Is a Probability Distribution? -- Types of Distributions -- Probability Mass Functions -- Probability Density Functions -- Mixed Distributions -- Equality and Equivalence of Random Variables -- Random Vectors and Bivariate Distributions -- Dependence and Independence of Random Variables -- The Law of Total Probability and Bayes' Theorem (Distributional Forms) -- Arithmetic Operations on Random Variables -- The Difference Between Sums and Mixtures -- Statistical Measures of Expectation, Variation, and Risk -- Expectation -- Deviation from Expectation -- Higher Moments -- Alternative Ways of Specifying Probability Distributions -- Moment and Cumulant Generating Functions -- Survival and Hazard Functions -- Appendix on Generalized Density Functions (Optional) -- Special Discrete Distributions.
Summary: This textbook for a one-semester course in probability covers combinatorial probability theory based on sets and counting, random variables and probability distribution, special discrete and continuous distributions, and transformations of random variables. A separate chapter provides four extended examples that apply many of the key concepts. Anno
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Includes index.

What Is Probability? --
How Is Uncertainty Quantified? --
Probability in Engineering and the Sciences --
What Is Actuarial Science? --
What Is Financial Engineering? --
Interpretations of Probability --
Probability Modeling in Practice --
Outline of This Book --
A Survey of Some Basic Concepts Through Examples --
Payoff in a Simple Game --
Choosing Between Payoffs --
Future Lifetimes --
Simple and Compound Growth --
Classical Probability --
The Formal Language of Classical Probability --
Conditional Probability --
The Law of Total Probability --
Bayes' Theorem --
Appendix on Sets, Combinatorics, and Basic Probability Rules --
Random Variables and Probability Distributions --
Definitions and Basic Properties --
What Is a Random Variable? --
What Is a Probability Distribution? --
Types of Distributions --
Probability Mass Functions --
Probability Density Functions --
Mixed Distributions --
Equality and Equivalence of Random Variables --
Random Vectors and Bivariate Distributions --
Dependence and Independence of Random Variables --
The Law of Total Probability and Bayes' Theorem (Distributional Forms) --
Arithmetic Operations on Random Variables --
The Difference Between Sums and Mixtures --
Statistical Measures of Expectation, Variation, and Risk --
Expectation --
Deviation from Expectation --
Higher Moments --
Alternative Ways of Specifying Probability Distributions --
Moment and Cumulant Generating Functions --
Survival and Hazard Functions --
Appendix on Generalized Density Functions (Optional) --
Special Discrete Distributions.

This textbook for a one-semester course in probability covers combinatorial probability theory based on sets and counting, random variables and probability distribution, special discrete and continuous distributions, and transformations of random variables. A separate chapter provides four extended examples that apply many of the key concepts. Anno

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