introduction to probability and statistics for science, engineering, and finance

ISBN-13: 9781584888123 / Angielski / Twarda / 2008 / 680 str.

Walter A. Rosenkrantz

Opis

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.

Recenzje

"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

Spis treści

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
2^k 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.

O autorze

Walter A. Rosenkrantz