1st Edition

Introduction to Probability and Statistics for Science, Engineering, and Finance

ISBN 9781584888123
Published July 10, 2008 by Chapman and Hall/CRC
680 Pages 99 B/W Illustrations

USD $130.00

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Book Description

Integrating interesting and widely used concepts of financial engineering into traditional statistics courses, Introduction to Probability and Statistics for Science, Engineering, and Finance illustrates the role and scope of statistics and probability in various fields.

The text first introduces the basics needed to understand and create tables and graphs produced by standard statistical software packages, such as Minitab, SAS, and JMP. It then takes students through the traditional topics of a first course in statistics. Novel features include:

  • Applications of standard statistical concepts and methods to the analysis and interpretation of financial data, such as risks and returns
  • Cox–Ross–Rubinstein (CRR) model, also called the binomial lattice model, of stock price fluctuations
  • An application of the central limit theorem to the CRR model that yields the lognormal distribution for stock prices and the famous Black–Scholes option pricing formula
  • An introduction to modern portfolio theory
  • Mean-standard deviation diagram of a collection of portfolios
  • Computing a stock’s betavia simple linear regression
  • As soon as he develops the statistical concepts, the author presents applications to engineering, such as queuing theory, reliability theory, and acceptance sampling; computer science; public health; and finance. Using both statistical software packages and scientific calculators, he reinforces fundamental concepts with numerous examples.

    Table of Contents

    Data Analysis
    The Role and Scope of Statistics in Science and Engineering
    Types of Data: Examples from Engineering, Public Health, and Finance
    The Frequency Distribution of a Variable Defined on a Population
    Quantiles of a Distribution
    Measures of Location (Central Value) and Variability
    Covariance, Correlation, and Regression: Computing a Stock’s Beta
    Mathematical Details and Derivations
    Large Data Sets
    Probability Theory
    Sample Space, Events, Axioms of Probability Theory
    Mathematical Models of Random Sampling
    Conditional Probability and Bayes’ Theorem
    The Binomial Theorem
    Discrete Random Variables and Their Distribution Functions
    Discrete Random Variables
    Expected Value and Variance of a Random Variable
    The Hypergeometric Distribution 
    The Binomial Distribution
    The Poisson Distribution
    Moment Generating Function: Discrete Random Variables
    Mathematical Details and Derivations
    Continuous Random Variables and Their Distribution Functions
    Random Variables with Continuous Distribution Functions: Definition and Examples
    Expected Value, Moments, and Variance of a Continuous Random Variable
    Moment Generating Function: Continuous Random Variables
    The Normal Distribution: Definition and Basic Properties
    The Lognormal Distribution: A Model for the Distribution of Stock Prices
    The Normal Approximation to the Binomial Distribution
    Other Important Continuous Distributions
    Functions of a Random Variable
    Mathematical Details and Derivations
    Multivariate Probability Distributions
    The Joint Distribution Function: Discrete Random Variables
    The Multinomial Distribution
    Mean and Variance of a Sum of Random Variables
    Why Stock Prices Have a Lognormal Distribution: An Application of the Central Limit Theorem
    Modern Portfolio Theory
    Risk Free and Risky Investing
    Theory of Single and Multi-Period Binomial Options
    Black–Scholes Formula for Multi-Period Binomial Options
    The Poisson Process
    Applications of Bernoulli Random Variables to Reliability Theory
    The Joint Distribution Function: Continuous Random Variables
    Mathematical Details and Derivations
    Sampling Distribution Theory
    Sampling from a Normal Distribution
    The Distribution of the Sample Variance
    Mathematical Details and Derivations
    Point and Interval Estimation
    Estimating Population Parameters: Methods and Examples
    Confidence Intervals for the Mean and Variance
    Point and Interval Estimation for the Difference of Two Means
    Point and Interval Estimation for a Population Proportion
    Some Methods of Estimation
    Hypothesis Testing
    Tests of Statistical Hypotheses: Basic Concepts and Examples
    Comparing Two Populations
    Normal Probability Plots
    Tests Concerning the Parameter p of a Binomial Distribution
    Statistical Analysis of Categorical Data
    Chi Square Tests
    Contingency Tables
    Linear Regression and Correlation
    Method of Least Squares
    The Simple Linear Regression Model
    Model Checking
    Correlation Analysis
    Mathematical Details and Derivations
    Large Data Sets
    Multiple Linear Regression
    The Matrix Approach to Simple Linear Regression
    The Matrix Approach to Multiple Linear Regression
    Mathematical Details and Derivations
    Single-Factor Experiments: Analysis of Variance
    The Single Factor ANOVA Model
    Confidence Intervals for the Treatment Means; Contrasts
    Random Effects Model
    Mathematical Derivations and Details
    Design and Analysis of Multi-Factor Experiments
    Randomized Complete Block Designs
    Two-Factor Experiments with n > 1 Observations per Cell
    2k Factorial Designs
    Statistical Quality Control
    x and R Control Charts
    p charts and c charts
    Appendix: Tables
    Answers to Selected Odd-Numbered Problems
    Chapter Summary, Problems, and To Probe Further sections appear at the end of each chapter.

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    "The book provides a very well-written, comprehensive treatment of all the standard requirements for an introductory course … Summing Up: Highly recommended."
    CHOICE, February 2009