Essentials of Probability & Statistics for Engineers & Scientists
Description
For junior/senior undergraduates taking a one-semester probability and statistics course as applied to engineering, science, or computer science.
This text covers the essential topics needed for a fundamental understanding of basic statistics and its applications in the fields of engineering and the sciences. Interesting, relevant applications use real data from actual studies, showing how the concepts and methods can be used to solve problems in the field. Students using this text should have the equivalent of the completion of one semester of differential and integral calculus.
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Content
1. Introduction to Statistics and Probability
1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability
1.2 Sampling Procedures; Collection of Data
1.3 Discrete and Continuous Data.
1.4 Probability: Sample Space and Events
Exercises
1.5 Counting Sample Points
Exercises
1.6 Probability of an Event
1.7 Additive Rules
Exercises
1.8 Conditional Probability, Independence, and the Product Rule
Exercises
1.9 Bayes' Rule
Exercises
Review Exercises
2. Random Variables, Distributions, and Expectations
2.1 Concept of a Random Variable
2.2 Discrete Probability Distributions
2.3 Continuous Probability Distributions
Exercises
2.4 Joint Probability Distributions
Exercises
2.5 Mean of a Random Variable
Exercises
2.6 Variance and Covariance of Random Variables.
Exercises
2.7 Means and Variances of Linear Combinations of Random Variables
Exercises
Review Exercises
2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
3. Some Probability Distributions
3.1 Introduction and Motivation
3.2 Binomial and Multinomial Distributions
Exercises
3.3 Hypergeometric Distribution
Exercises
3.4 Negative Binomial and Geometric Distributions
3.5 Poisson Distribution and the Poisson Process
Exercises
3.6 Continuous Uniform Distribution
3.7 Normal Distribution
3.8 Areas under the Normal Curve
3.9 Applications of the Normal Distribution
Exercises
3.10 Normal Approximation to the Binomial
Exercises
3.11 Gamma and Exponential Distributions
3.12 Chi-Squared Distribution.
Exercises
Review Exercises
3.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
4. Sampling Distributions and Data Descriptions
4.1 Random Sampling
4.2 Some Important Statistics
Exercises
4.3 Sampling Distributions
4.4 Sampling Distribution of Means and the Central Limit Theorem
Exercises
4.5 Sampling Distribution of S2
4.6 t -Distribution
4.7 F -Distribution
4.8 Graphical Presentation
Exercises
Review Exercises
4.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
5. One- and Two-Sample Estimation Problems
5.1 Introduction
5.2 Statistical Inference
5.3 Classical Methods of Estimation.
5.4 Single Sample: Estimating the Mean
5.5 Standard Error of a Point Estimate
5.6 Prediction Intervals
5.7 Tolerance Limits
Exercises
5.8 Two Samples: Estimating the Difference between Two Means
5.9 Paired Observations
Exercises
5.10 Single Sample: Estimating a Proportion
5.11 Two Samples: Estimating the Difference between Two Proportions
Exercises
5.12 Single Sample: Estimating the Variance
Exercises
Review Exercises
5.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
6. One- and Two-Sample Tests of Hypotheses.
6.1 Statistical Hypotheses: General Concepts
6.2 Testing a Statistical Hypothesis
6.3 The Use of P-Values for Decision Making in Testing Hypotheses
Exercises
6.4 Single Sample: Tests Concerning a Single Mean
6.5 Two Samples: Tests o