Introduction to Probability and Statistics for Science, Engineering, and Finance: 1st Edition (Hardback) book cover

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

1st Edition

By Walter A. Rosenkrantz

Chapman and Hall/CRC

680 pages | 99 B/W Illus.

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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.

    Reviews

    "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

    Table of Contents

    Data Analysis

    Orientation

    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

    Orientation

    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

    Orientation

    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

    Orientation

    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

    Orientation

    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

    Orientation

    Sampling from a Normal Distribution

    The Distribution of the Sample Variance

    Mathematical Details and Derivations

    Point and Interval Estimation

    Orientation

    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

    Orientation

    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

    Orientation

    Chi Square Tests

    Contingency Tables

    Linear Regression and Correlation

    Orientation

    Method of Least Squares

    The Simple Linear Regression Model

    Model Checking

    Correlation Analysis

    Mathematical Details and Derivations

    Large Data Sets

    Multiple Linear Regression

    Orientation

    The Matrix Approach to Simple Linear Regression

    The Matrix Approach to Multiple Linear Regression

    Mathematical Details and Derivations

    Single-Factor Experiments: Analysis of Variance

    Orientation

    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

    Orientation

    Randomized Complete Block Designs

    Two-Factor Experiments with n > 1 Observations per Cell

    2k Factorial Designs

    Statistical Quality Control

    Orientation

    x and R Control Charts

    p charts and c charts

    Appendix: Tables

    Answers to Selected Odd-Numbered Problems

    Index

    Chapter Summary, Problems, and To Probe Further sections appear at the end of each chapter.

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT000000
    MATHEMATICS / General
    MAT029000
    MATHEMATICS / Probability & Statistics / General
    MAT029010
    MATHEMATICS / Probability & Statistics / Bayesian Analysis
    TEC029000
    TECHNOLOGY & ENGINEERING / Operations Research