Probability and Statistics for STEM: A Course in One Semester

Description

One of the most important subjects for all engineers and scientists is probability and statistics. This book presents the basics of the essential topics in probability and statistics from a rigorous standpoint. The basics of probability underlying all statistics is presented first and then we cover the essential topics in statistics, confidence intervals, hypothesis testing, and linear regression. This book is suitable for any engineer or scientist who is comfortable with calculus and is meant to be covered in a one-semester format. Preface Acknowledgments Probability The Basics Conditional Probability Appendix: Counting Problems Random Variables Distributions Important Discrete Distributions Important Continuous Distributions Expectation, Variance, Medians, Percentiles Moment-Generating Functions Mean and Variance of Some Important Distributions Joint Distributions Independent Random Variables Covariance and Correlation The General Central Limit Theorem Chebychev's Inequality and the Weak Law of Large Numbers 2(k), Student's t- and F-Distributions 2(k) Distribution Student's t-Distribution F-Distribution Problems Distributions of Sample Mean and Sample SD Population Distribution Known The Population X N(,) The Population X is not Normal but has Known Mean and Variance The Population is Bernoulli, p Known Population Variance Unknown: Sampling Distribution of the Sample Variance Sampling Distribution of Differences of Two Samples Problems Confidence and Prediction Intervals Confidence Intervals for a Single Sample Controlling the Error of an Estimate Using Confidence Intervals Pivotal Quantities Confidence Intervals for the Mean and Variance of a Normal Distribution Confidence Intervals for a Proportion One-Sided Confidence Intervals Confidence Intervals for Two Samples Difference of Two Normal Means Ratio of Two Normal Variances Difference of Two Binomial Proportions Paired Samples Prediction Intervals Problems Hypothesis Testing A Motivating Example The Basics of Hypothesis Testing Hypotheses Tests for One Parameter Hypotheses Tests for the Normal Parameters, Critical Value Approach The p-Value Approach to Hypothesis Testing Test of Hypotheses for Proportions Hypotheses Tests for Two Populations Test of Hypotheses for Two Proportions Power of Tests of Hypotheses Factors Affecting Power of a Test of Hypotheses Power of One-Sided Tests More Tests of Hypotheses Chi-Squared Statistic and Goodness-of-Fit Tests Contingency Tables and Tests for Independence Analysis of Variance Problems Summary Tables Linear Regression Introduction and Scatter Plots Introduction to Regression The Linear Model with Observed X Estimating the Slope and Intercept from Data Errors of the Regression The Distributions of and Confidence Intervals for Slope and Intercept and Hypothesis Tests Confidence and Prediction Bands Hypothesis Test for the Correlation Coefficient Problems Answers to Problems Answers to Chapter 1 Problems Answers to Chapter 2 Problems Answers to Chapter 3 Problems Answers to Chapter 4 Problems Answers to Chapter 5 Problems Answers to Chapter 6 Problems Authors' Biographies Index Blank Page