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

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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.show more

## Product details

- Electronic book text | 680 pages
- 10 Jul 2008
- Taylor & Francis Ltd
- Chapman & Hall/CRC
- London, United Kingdom
- 1000 equations; 199 Tables, black and white; 99 Illustrations, black and white
- 158488813X
- 9781584888130

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## 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.show more