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E-raamat: Introduction to Probability and Statistics for Science, Engineering, and Finance

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(University of Massachusetts, Amherst, USA)
  • Formaat: 680 pages
  • Ilmumisaeg: 10-Jul-2008
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781584888130
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Introduction to Probability and Statistics for Science, Engineering, and FinanceSuurem pilt
  • Formaat: 680 pages
  • Ilmumisaeg: 10-Jul-2008
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781584888130
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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 CoxRossRubinstein (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 BlackScholes option pricing formula An introduction to modern portfolio theory Mean-standard deviation diagram of a collection of portfolios Computing a stocks 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.

Arvustused

"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

Data Analysis
1(70)
Orientation
1(1)
The Role and Scope of Statistics in Science and Engineering
2(3)
Types of Data: Examples from Engineering, Public Health, and Finance
5(12)
Univariate Data
5(2)
Multivariate Data
7(2)
Financial Data: Stock Market Prices and Their Time Series
9(4)
Stock Market Returns: Definition and Examples
13(4)
The Frequency Distribution of a Variable Defined on a Population
17(9)
Organizing the Data
17(1)
Graphical Displays
18(4)
Histograms
22(4)
Quantiles of a Distribution
26(6)
The Median
26(1)
Quantiles of the Empirical Distribution Function
27(5)
Measures of Location (Central Value) and Variability
32(6)
The Sample Mean
32(1)
Sample Standard Deviation: A Measure of Risk
33(3)
Mean-Standard Deviation Diagram of a Portfolio
36(1)
Linear Transformations of Data
37(1)
Covariance, Correlation, and Regression: Computing a Stock's Beta
38(5)
Fitting a Straight line to Bivariate Data
40(3)
Mathematical Details and Derivations
43(1)
Chapter Summary
44(1)
Problems
44(21)
Large Data Sets
65(5)
To Probe Further
70(1)
Probability Theory
71(42)
Orientation
71(1)
Sample Space, Events, Axioms of Probability Theory
72(12)
Probability Measures
78(6)
Mathematical Models of Random Sampling
84(10)
Multinomial Coefficients
93(1)
Conditional Probability and Bayes' Theorem
94(6)
Conditional Probability
94(3)
Bayes' Theorem
97(2)
Independence
99(1)
The Binomial Theorem
100(1)
Chapter Summary
101(1)
Problems
101(10)
To Probe Further
111(2)
Discrete Random Variables and Their Distribution Functions
113(48)
Orientation
113(1)
Discrete Random Variables
114(7)
Functions of a Random Variable
120(1)
Expected Value and Variance of a Random Variable
121(9)
Moments of a Random Variable
125(3)
Variance of a Random Variable
128(2)
Chebyshev's Inequality
130(1)
The hypergeometric Distribution
130(4)
The Bionomial Distribution
134(10)
A Coin Tossing Model for Stock Market Returns
140(4)
The Poisson Distribution
144(2)
Moment Generating Function: Discrete Random Variables
146(2)
Mathematical Details and Derivations
148(2)
Chapter Summary
150(1)
Problems
151(9)
To Probe Further
160(1)
Continuous Random Variables and Their Distribution Functions
161(44)
Orientation
161(1)
Random Variables with Continuous Distribution Functions: Definition And Examples
162(5)
Expected Value, Moments, and Variance of a Continuous Random Variable
167(4)
Moment Generating Functions: Continuous Random Variables
171(1)
The Normal Distribution: Definition and Basic Properties
172(5)
The lognormal Distribution: A Model for the Distributions of Stock Prices
177(2)
The Normal Approximation to the Binomial Distribution
179(6)
Distribution of the Sample Proportion p
185(1)
Other Important Continuous Distributions
185(4)
The Gamma and Chi-Square Distributions
185(3)
The Weibull Distribution
188(1)
The Beta Distribution
188(1)
Functions of a Random Variable
189(2)
Mathematical Details and Derivations
191(1)
Chapter Summary
192(1)
Problems
192(10)
To Probe Further
202(3)
Multivariate Probability Distributions
205(72)
Orientation
205(1)
The Joint Distribution: Discrete Random Variables
206(6)
Independent Random Variables
211(1)
The Multinomial Distribution
212(1)
Mean and Variance of a Sum of Random Variables
213(9)
The Law of Large Numbers for Sums of Independent and Identically Distributed (iid) Random Variables
220(2)
The Central Limit Theorem
222(1)
Why Stock Price Have a Lognormal Distribution: An Application of the Central Limit Theorem
222(8)
The Bionomial Lattice Model as an Approximation to a Continuous Time Model for Stock Market Prices
227(3)
Modern Portfolio Theory
230(2)
Mean-Variance Analysis of a Portfolio
230(2)
Risk Free and Risky Investing
232(5)
Present Value Analysis of Risk Free and Risky Returns
232(3)
Present Value Analysis of Deterministic and Random Cash Flows
235(2)
Theory of Single and Multi-Period Binomial Options
237(3)
Black-Scholes Option Pricing Formula: Binomil Options
237(3)
Black-Scholes Pricing Formula for Multi-Period Binomial Options
240(3)
Black-Scholes Pricing Formula for Stock Prices Governed by a Log-normal Distribution
242(1)
The Poisson Process
243(5)
The Poisson Process and the Gamma Distribution
246(2)
Applications of bernoulli Random Variables to Reliability Theory
248(3)
The joint Distribution Function: Continuous Random Variables
251(7)
Functions of Random Vectors
254(2)
Conditional Distributions and Conditional Expectations: Continuous Case
256(1)
The Bivariate Normal Distribution
257(1)
Mathematical Details and Derivations
258(5)
Chapter Summary
263(1)
Problems
263(12)
To Probe Further
275(2)
Sampling Distribution Theory
277(14)
Orientation
277(1)
Sampling from a Normal Distribution
277(5)
The Distribution of the Sample Variance
282(4)
Student's t Distribution
285(1)
The F Distribution
285(1)
Mathematical Details and Derivations
286(1)
Chapter Summary
287(1)
Problems
287(3)
To Probe Further
290(1)
Point and Interval Estimation
291(34)
Orientation
291(1)
Estimating Population Parameters: Methods and Examples
292(4)
Some Properties of Estimators: Bias, Variance, and Consistency
294(2)
Confidence Intervals for the Mean and Variance
296(8)
Confidence Intervals for the Mean of a Normal Distribution: Variance Unknown
299(1)
Confidence Intervals for the Mean of an Arbitrary Distribution
300(2)
Confidence Intervals for the Variance of a Normal Distribution
302(1)
Value at Risk (VaR): An Application of Confidence Intervals to Risk Management
303(1)
Point and interval Estimation for the Difference of Two Means
304(3)
Paired Samples
305(2)
Point and Interval Estimation for a Population Proportion
307(3)
Confidence Intervals for p1---p2
309(1)
Some Methods of Estimation
310(6)
Method of Moments
310(2)
Maximum Likelihood Estimators
312(4)
Chapter Summary
316(1)
Problems
316(8)
To Probe Further
324(1)
Hypothesis Testing
325(48)
Orientation
325(1)
Tests of Statistical Hypotheses: Basic Concept and Examples
326(18)
Significance Testing
336(2)
Power Function and Sample Size
338(1)
Large Sample Tests Concerning the Mean of an Arbitrary Distribution
339(1)
Tests Concerning the Mean of a Distribution with Unknown Variance
340(4)
Comparing Two Populations
344(7)
The Wilcoxon Rank Sum Test for Two Independent Samples
347(3)
A Test of the Equality of Two Variances
350(1)
Normal Probability Plots
351(4)
Tests Concerning the Parameter P of a Binomial Distribution
355(5)
Tests of Hypotheses Concerning Two Binomial Distributions: Large Sample Size
359(1)
Chapter Summary
360(1)
Problems
361(11)
To Probe Further
372(1)
Statistical Analysis of Categorical Data
373(16)
Orientation
373(1)
Chi-Square Tests
373(4)
Chi-Square Tests When the Cell probabilities are Not Completely Specified
376(1)
Contingency Tables
377(6)
Chapter Summary
383(1)
Problems
383(5)
To Probe Further
388(1)
Linear Regression and Correlation
389(52)
Orientation
389(1)
Method of Least Squares
390(8)
Fitting a Straight Line via Ordinary Least Squares
392(6)
The Simple Linear Regression Model
398(13)
The Sampling Distribution of β1, β0, SSE, and SSR
399(7)
Tests of Hypothese Concerning the Regression Analysis in an ANOVA Table
406
Confidence Intervals and Prediction Intervals
403(3)
Displaying the Output of a Regression Analysis in an ANOVA Table
406(2)
Curviliner Regression
408(3)
Model Checking
411(5)
Correlation Analysis
416(6)
Computing the Market Risk of a Stock
417(4)
The Shapiro-Wilk Test for Normality
421(1)
Mathematical Details and Derivations
422(4)
Chapter Summary
426(1)
Problems
426(11)
Large Data Sets
437(2)
To Probe Further
439(2)
Multiple Linear Regression
441(28)
Orientation
441(1)
The Matrix Approach to Simple Linear Regression
442(8)
Sampling Distribution of the Least Squares Solution
447(2)
Geometric Interpretation of the Least Squares Solution
449(1)
The Matrix Approach to Multiple Linear Regression
450(14)
Normal Equations Fitted Values, and ANOVA Table for the Multiple Linear Regression Model
454(3)
Testing Hypotheses about the Regression Model
457(3)
Model Checking
460(2)
Confidence Intervals and Prediction intervals in Multiple Regression
462(2)
Mathematical Details and Derivations
464(1)
Chapter Summary
464(1)
Problems
465(3)
To Probe Further
468(1)
Single Factor Experiments: Analysis of Variance
469(28)
Orientation
469(1)
The single Factor ANOVA Model
469(16)
Estimating the ANOVA Model Parameters
473(2)
Testing Hypotheses about the Parameters
475(3)
Model Checking via Residual Plots
478(2)
Unequal Sample Sizes
480(5)
Confidence Intervals for the Treatment Means
485(2)
Multiple Comparisons of Treatment Means
485(2)
Random Effects Model
487(2)
Mathematical Dervations and Details
489(1)
Chapter Summary
490(1)
Problems
490(6)
To Probe Further
496(1)
Design and Analysis of Multi-Factor Experiments
497(54)
Orientation
497(1)
Randomized Complete Block Designs
498(10)
Confidence Intervals and Multiple Comparison Procedures
507(1)
Model Checking via Residual Plots
508(1)
Two Factor Experiments with η > 1 Observations per Cell
508(14)
Confidence Intervals and Multiple Comparison Procedures
520(2)
2K Factorial Designs
522(18)
Chapter Summary
540(1)
Problems
540(8)
To Probe Further
548(3)
Statistical Quality control
551(16)
Orientation
551(1)
x and R Control Chart
552(7)
Detecting a Shift in the Process Mean
557(2)
P Charts and C Charts
559(3)
Chapter Summary
562(1)
Problems
562(3)
To Probe Further
565(2)
Tables
567(22)
Cumulative Bionomial Distribution
568(2)
Cumulative Poisson Distribution
570(2)
Standard Normal Probablities
572(2)
Critical Values tv(α) of the Distribution
574(1)
Quantiles Qv(P) = X2v(1-P) of the X2 Distribution
575(1)
Critical Values of the Fv1, v2 (α) Distribution
576(4)
Critical Values of the Studentized Range q(αην)
580(4)
Factors for Estimating σ s, or σ RMS and σ R from R
584(2)
Factors for determining from σ the Three-Sigma Control Limits for X, R, Aand s or σRMS Charts
586(3)
Answers to selected Odd-Numebered Problems
589(72)
Data Analysis
591(6)
Probability Theory
597(4)
Discrete Random Variables and their Distribution Functions
601(8)
Continuous Random Variables and Their Distribution Functions
609(8)
Multivariate Probability Distributions
617(6)
Sampling Distribution Theory
623(2)
Point and interval Estimation
625(6)
Hypothesis Testing
631(6)
Statistical Analysis of Categorical Data
637(4)
Linear Regression and Correlation
641(4)
Multiple Linear Regression
645(2)
Single Factor Experiments: Analysis of Variance
647(6)
Design and Analysis of Multi-Factor Experiments
653(6)
Statistical Quality Control
659(2)
Index 661
Walter A. Rosenkrantz
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