Essentials of Probability & Statistics for Engineers & Scientists

<p>1. Introduction to Statistics and Probability</p> <p>1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability</p> <p>1.2 Sampling Procedures; Collection of Data</p> <p>1.3 Discrete and Continuous Data.</p> <p>1.4 Probability: Sample Space and Events</p> <p>&nbsp;&nbsp; Exercises</p> <p>1.5 Counting Sample Points</p> <p>&nbsp;&nbsp; Exercises</p> <p>1.6 Probability of an Event</p> <p>1.7 Additive Rules</p> <p>&nbsp;&nbsp; Exercises</p> <p>1.8 Conditional Probability, Independence, and the Product Rule</p> <p>&nbsp;&nbsp; Exercises</p> <p>1.9 Bayes' Rule</p> <p>&nbsp;&nbsp; Exercises</p> <p>&nbsp;&nbsp; Review Exercises</p> <p>&nbsp;</p> <p>2. Random Variables, Distributions, and Expectations</p> <p>2.1 Concept of a Random Variable</p> <p>2.2 Discrete Probability Distributions</p> <p>2.3 Continuous Probability Distributions</p> <p>&nbsp;&nbsp; Exercises</p> <p>2.4 Joint Probability Distributions</p> <p>&nbsp;&nbsp; Exercises</p> <p>2.5 Mean of a Random Variable</p> <p>&nbsp;&nbsp; Exercises</p> <p>2.6 Variance and Covariance of Random Variables.</p> <p>&nbsp;&nbsp; Exercises</p> <p>2.7 Means and Variances of Linear Combinations of Random Variables</p> <p>&nbsp;&nbsp; Exercises</p> <p>&nbsp;&nbsp; Review Exercises</p> <p>2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters</p> <p>&nbsp;</p> <p>3. Some Probability Distributions</p> <p>3.1 Introduction and Motivation</p> <p>3.2 Binomial and Multinomial Distributions</p> <p>&nbsp;&nbsp; Exercises</p> <p>3.3 Hypergeometric Distribution</p> <p>&nbsp;&nbsp; Exercises</p> <p>3.4 Negative Binomial and Geometric Distributions</p> <p>3.5 Poisson Distribution and the Poisson Process</p> <p>&nbsp;&nbsp; Exercises</p> <p>3.6 Continuous Uniform Distribution</p> <p>3.7 Normal Distribution</p> <p>3.8 Areas under the Normal Curve</p> <p>3.9 Applications of the Normal Distribution</p> <p>&nbsp;&nbsp; Exercises</p> <p>3.10 Normal Approximation to the Binomial</p> <p>&nbsp;&nbsp; Exercises</p> <p>3.11 Gamma and Exponential Distributions</p> <p>3.12 Chi-Squared Distribution.</p> <p>&nbsp;&nbsp; Exercises</p> <p>&nbsp;&nbsp; Review Exercises</p> <p>3.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters</p> <p>&nbsp;</p> <p>4. Sampling Distributions and Data Descriptions</p> <p>4.1 Random Sampling</p> <p>4.2 Some Important Statistics</p> <p>&nbsp;&nbsp; Exercises</p> <p>4.3 Sampling Distributions</p> <p>4.4 Sampling Distribution of Means and the Central Limit Theorem</p> <p>&nbsp;&nbsp; Exercises</p> <p>4.5 Sampling Distribution of S2</p> <p>4.6 t-Distribution</p> <p>4.7 F-Distribution</p> <p>4.8 Graphical Presentation</p> <p>&nbsp;&nbsp; Exercises</p> <p>&nbsp;&nbsp; Review Exercises</p> <p>4.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters</p> <p>&nbsp;</p> <p>5. One- and Two-Sample Estimation Problems</p> <p>5.1 Introduction</p> <p>5.2 Statistical Inference</p> <p>5.3 Classical Methods of Estimation.</p> <p>5.4 Single Sample: Estimating the Mean</p> <p>5.5 Standard Error of a Point Estimate</p> <p>5.6 Prediction Intervals</p> <p>5.7 Tolerance Limits</p> <p>&nbsp;&nbsp; Exercises</p> <p>5.8 Two Samples: Estimating the Difference between Two Means</p> <p>5.9 Paired Observations</p> <p>&nbsp;&nbsp; Exercises</p> <p>5.10 Single Sample: Estimating a Proportion</p> <p>5.11 Two Samples: Estimating the Difference between Two Proportions</p> <p>&nbsp;&nbsp; Exercises</p> <p>5.12 Single Sample: Estimating the Variance</p> <p>&nbsp;&nbsp; Exercises</p> <p>&nbsp;&nbsp; Review Exercises</p> <p>5.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters</p> <p>&nbsp;</p> <p>6. One- and Two-Sample Tests of Hypotheses.</p> <p>6.1 Statistical Hypotheses: General Concepts</p> <p>6.2 Testing a Statistical Hypothesis</p> <p>6.3 The Use of P-Values for Decision Making in Testing Hypotheses</p> <p>&nbsp;&nbsp; Exercises</p> <p>6.4 Single Sample: Tests Concerning a Single Mean</p> <p>6.5 Two Samples: Tests o</p>