TAILIEUCHUNG - An Introduction to Statistical Inference and Data Analysis

This chapter collects some fundamental mathematical concepts that we will use in our study of probability and statistics. Most of these concepts should seem familiar, although our presentation of them may be a bit more formal than you have previously encountered. This formalism will be quite useful as we study probability, but it will tend to recede into the background as we progress to the study of statistics. | An Introduction to Statistical Inference and Data Analysis Michael W. Trosset1 April 3, 2001 1Department of Mathematics, College of William & Mary, . Box 8795, Williamsburg, VA 23187-8795. Contents 1 Mathematical Preliminaries 5 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Probability 17 Interpretations of Probability . . . . . . . . . . . . . . . . . . 17 Axioms of Probability . . . . . . . . . . . . . . . . . . . . . . 18 Finite Sample Spaces . . . . . . . . . . . . . . . . . . . . . . . 26 Conditional Probability . . . . . . . . . . . . . . . . . . . . . 32 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 43 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3 Discrete Random Variables 55 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Binomial Distributions . . . . . . . . . . . . . . . . . . . . . . 72 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4 Continuous Random Variables 81 A Motivating Example . . . . . . . . . . . . . . . . . . . . . . 81 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Elementary Examples . . . . . . . . . . . . . . . . . . . . . . 88 Normal Distributions . . . . . . . . . . . . . . . . . . . . . . . 93 Normal Sampling Distributions . . . . . . . . . . . . . . . . . 97 1 2 CONTENTS Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5 Quantifying Population Attributes 105 .

• Toán học
• Statistical Inferenc
• Data Analysis
• Mathematical Preliminarie
• Sample Location Problem
• statistics
• Michael W
• Trosset