Probability and statistics : based on Schaum's Outline of probability and statistics by Murray R. Spiegel, John Schiller, and R. Alu Srinivasan

If you are looking for a quick nuts-and-bolts overview, turn to Schaum's Easy Outlines!Schaum's Easy Outline of Probability and Statistics is a pared-down, simplified, and tightly focused review of the topic. With an emphasis on clarity and brevity, it features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give you quick pointers to the essentials.Expert tips for mastering probability and statistics Last-minute essentials to pass the course Coverage of all course fundamentals Easy to understand methodology Clear, concise explanations of all probability and statistics concepts Appropriate for the following courses: Introduction to Probability & Statistics, Probability, Business Statistics, Basic Statistics, and Beginning Statistics Easily understood review of basic probability and statistics principles About the AuthorJohn J. Schiller is an associate professor of mathematics at Temple University. He received his Ph.D. at the University of Pennsylvania. He has published research papers in the areas of Riemann surfaces, discrete mathematics, and mathematical biology. He has also coauthored several other mathematics texts. R. Alu Srinivasan is a professor of mathematics at Temple University. He received his Ph.D. at Wayne State University and has published extensively in probability and statistics.The late Murray R. Spiegel was professor and chairman of mathematics at the Rensselaer Polytechnic Institute, Hartford Graduate Center, in Troy, New York. During his career, he held positions at Harvard University, Cornell University, and Oak Ridge. He was the author of numerous journal articles and 14 books on various topics in mathematics. [C:\Users\Microsoft\Documents\Calibre Library] Copyright 5 Contents 7 Chapter 1 BASIC PROBABILITY 9 Random Experiments 10 Sample Spaces 10 Events 11 The Concept of Probability 12 The Axioms of Probability 12 Some Important Theorems on Probability 13 Assignment of Probabilities 14 Conditional Probability 15 Theorem on Conditional Probability 15 Independent Events 16 Bayes’ Theorem or Rule 17 Combinatorial Analysis 17 Fundamental Principle of Counting 18 Permutations 18 Combinations 19 Binomial Coefficients 20 Stirling’s Approximation to n! 20 Chapter 2 DESCRIPTIVE STATISTICS 22 Descriptive Statistics 22 Measures of Central Tendency 23 Mean 23 Median 24 Mode 25 Measures of Dispersion 26 Variance and Standard Deviation 26 Percentiles 28 Interquartile Range 28 Skewness 29 Chapter 3 DISCRETE RANDOM VARIABLES 31 Random Variables 31 Discrete Probability Distribution 32 Distribution Functions for Random Variables 33 Distribution Functions for Discrete Random Variables 34 Expected Values 35 Variance and Standard Deviation 36 Some Theorems on Expectation 38 Some Theorems on Variance 38 Chapter 4 CONTINUOUS RANDOM VARIABLES 42 Continuous Random Variables 42 Continuous Probability Distribution 43 Distribution Functions for Continuous Random Variables 44 Expected Values 46 Variance 46 Properties of Expected Values and Variances 47 Graphical Interpretations 49 Chapter 5 EXAMPLES OF RANDOM VARIABLES 50 Binomial Distribution 51 Properties of Binomial Distributions 52 The Normal Distribution 53 Examples of the Normal Distribution 55 Poisson Distributions 59 Relationships between Binomial and Normal Distributions 60 Relationships between Binomial and Poisson Distributions 62 Relationships between Poisson and Normal Distributions 63 Central Limit Theorem 64 Law of Large Numbers 64 Chapter 6 SAMPLING THEORY 66 Population and Sample 67 Sampling 67 Random Samples, Random Numbers 68 Population Parameters 68 Sample Statistics 69 Sampling Distributions 71 The Sample Mean 72 Sampling Distribution of Means 72 Sampling Distribution of Proportions 75 Sampling Distribution of Differences and Sums 76 The Sample Variance 79 Frequency Distributions 80 Relative Frequency Distributions 81 Chapter 7 ESTIMATION THEORY 83 Unbiased Estimates and Ef.cient Estimates 83 Point Estimates and Interval Estimates 84 Confidence Interval Estimates of Population Parameters 84 Confidence Intervals for Means 86 Confidence Intervals for Proportions 89 Confidence Intervals for Differences and Sums 90 Chapter 8 TEST OF HYPOTHESIS AND SIGNIFICANCE 93 Statistical Decisions 93 Statistical Hypothesis 94 Tests of Hypothesis and Signi.cance 94 Type I and Type II Errors 95 Level of Significance 95 Test Involving the Normal Distribution 96 One-Tailed and Two-Tailed Tests 98 P Value 98 Special Tests 101 Relationship between Estimation Theory and Hypothesis Testing 105 Chapter 9 CURVE FITTING, REGRESSION, AND CORRELATION 107 Curve Fitting 108 Regression 110 The Method of Least Squares 110 The Least-Squares Line 112 The Least-Squares Regression Line in Terms of Sample Variances and Covariance 116 Standard Error of Estimate 118 The Linear Correlation Coef.cient 119 Generalized Correlation Coef.cient 122 Correlation and Dependence 123 Chapter 10 OTHER PROBABILITY DISTRIBUTIONS 125 The Multinomial Distribution 126 The Hypergeometric Distribution 126 The Uniform Distribution 129 The Cauchy Distribution 129 The Gamma Distribution 130 The Beta Distribution 130 The Chi-Square Distribution 131 Student’s t Distribution 134 The F Distribution 136 Relationships Among Chi-Square, t, and F Distributions 138 Appendix A 140 Special Sums 140 Eulers’ Formulas 141 The Gamma Function 141 The Beta Function 142 Special Integrals 142 Appendix B 144 Appendix C 146 Appendix D 148 Appendix E 150 Appendix F 154 Appendix G 156 Index 157 Boiled-down essentials of the top-selling Schaum's Outline series for the student with limited time What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials. Designed to appeal to underprepared students and readers turned off by dense text Cartoons, sidebars, icons, and other graphic pointers get the material across fast Concise text focuses on the essence of the subject Delivers expert help from teachers who are authorities in their fields Perfect for last-minute test preparation So small and light that they fit in a backpack! Confusing Textbooks? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives youPractice problems with full explanations that reinforce knowledgeCoverage of the most up-to-date developments in your course fieldIn-depth review of practices and applicationsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Suitable for last-minute test preparation, this title features graphic elements such as sidebars, reader-alert icons, and boxed highlights that stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials. A Guide To Probability And Mathematical Statistics Featuring Solved Exercises And Study Tips. By Murray Spiegel, John Schiller, And Alu Srinivasan. Includes Index. We are all familiar with the importance of experiments in science and engineering.