A First Course in Probability Models and Statistical Inference

Welcome to new territory: A course in probability models and statistical inference. The concept of probability is not new to you of course. You've encountered it since childhood in games of chance-card games, for example, or games with dice or coins. And you know about the "90% chance of rain" from weather reports. But once you get beyond simple expressions of probability into more subtle analysis, it's new territory. And very foreign territory it is. You must have encountered reports of statistical results in voter sur veys, opinion polls, and other such studies, but how are conclusions from those studies obtained? How can you interview just a few voters the day before an election and still determine fairly closely how HUN DREDS of THOUSANDS of voters will vote? That's statistics. You'll find it very interesting during this first course to see how a properly designed statistical study can achieve so much knowledge from such drastically incomplete information. It really is possible-statistics works! But HOW does it work? By the end of this course you'll have understood that and much more. Welcome to the enchanted forest.

Klappentext

This textbook provides an introductory course in probability and statistical inference. Its emphasis in the probability portion of the text is on developing a clear and concrete understanding of probability distributions as models for real-world situations. This understanding of probability distributions is then used to develop the basic principles of statistical inference and to apply these ideas in a wide variety of applications. A particular feature of the book is the author's use of exercises to develop the reader's understanding of important concepts. Each exercise comes with two levels of solutions: the first level consists of hints, clarifications, and references to relevant discussions in the text; while the second level provides detailed and complete solutions. The author presupposes no previous knowledge on the half of the reader and carefully discusses each of the main concepts from probability and statistics as they are introduced. As a result, this book makes an excellent introduction to this central component of any curriculum which includes quantitative methods.

Inhalt
1 Introduction to Probability Models of the Real World.- 1.1 Probability Distributions of Random Variables.- 1.2 Parameters to Characterize a Probability Distribution.- 1.3 Linear Functions of a Random Variable.- 1.4 The Fundamentals of Probability Theory.- 1.5 Some Review Exercises.- 2 Understanding Observed Data.- 2.1 Observed Data from the Real World.- 2.2 Presenting and Summarizing Observed Numeric Data.- 2.3 Grouped Data: Suppressing Irrelevant Detail.- 2.4 Using the Computer.- 3 Discrete Probability Models.- 3.1 Introduction.- 3.2 The Discrete Uniform Distribution.- 3.3 The Hypergeometric Distribution.- 3.4 Sampling with Replacement from a Dichotomous Population.- 3.5 The Bernoulli Trial.- 3.6 The Geometric Distribution.- 3.7 The Binomial Distribution.- 3.8 The Poisson Distribution.- 3.9 The Negative Binomial Distribution.- 3.10 Some Review Problems.- 4 Continuous Probability Models.- 4.1 Continuous Distributions and the Continuous Uniform Distribution.- 4.2 The Exponential Distribution.- 4.3 The Normal Distribution.- 4.4 The Chi-Squared Distribution.- 4.5 A Few Review Problems.- 5 Estimation of Parameters.- 5.1 Parameters and Their Estimators.- 5.2 Estimating an Unknown Proportion.- 5.3 Estimating an Unknown Mean.- 5.4 A Confidence Interval Estimate for an Unknown ?.- 5.5 One-Sided Intervals, Prediction Intervals, Tolerance Intervals.- 6 Introduction to Tests of Statistical Hypotheses.- 6.1 Introduction.- 6.2 Tests of Significance.- 6.3 Hypothesis Tests.- 6.4 A Somewhat Comprehensive Review.- 7 Introduction to Simple Linear Regression.- 7.1 The Simple Linear Regression Model.- 7.2 The Least Squares Estimates for ? and ?.- 7.3 Using the Simple Linear Regression Model.- 7.4 Some Review Problems.- Answers to Try Your HandLevel 1.-Answers to Try Your HandLevel II.- Tables.- The Standard Normal Distribution.- The Chi-Squared Distribution.- Index of Notation.- Author Index.