401txt - Statistics 401: An Introduction to Statistics for...

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Unformatted text preview: Statistics 401: An Introduction to Statistics for Engineers and Scientists Michael G. Akritas Penn State University Fall 2006 Contents 1 Basic Statistical Concepts 1 1.1 Why Statistics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Populations and Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Random Variables and Statistical Populations . . . . . . . . . . . . . . . . 4 1.4 Population Average and Sample Average . . . . . . . . . . . . . . . . . . . 6 1.5 Statistical Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Some Sampling Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6.1 Representative Samples . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6.2 Simple Random Sampling, and Stratified Sampling . . . . . . . . . 11 1.6.3 Sampling With and Without Replacement . . . . . . . . . . . . . . 13 1.6.4 Non-representative Sampling . . . . . . . . . . . . . . . . . . . . . . 14 1.7 Statistical Experiments and Observational Studies . . . . . . . . . . . . . . 15 1.8 The Role of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.9 Approaches to Statistical Inference . . . . . . . . . . . . . . . . . . . . . . 18 1.10 Exercises for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Introduction to Probability 22 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Sample Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Events and Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 II 2.4 Interpretation and Properties of Probability . . . . . . . . . . . . . . . . . 27 2.5 Independent Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.7 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.7.1 The Law of Total Probability . . . . . . . . . . . . . . . . . . . . . 42 2.7.2 Bayes Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.8 Exercises for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3 Random Variables and Their Distributions 50 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3.1 The cumulative distribution function . . . . . . . . . . . . . . . . . 54 3.3.2 The probability mass function of a discrete distribution . . . . . . . 57 3.3.3 The probability density function of a continuous distribution . . . . 60 3.4 Parameters of a Univariate Distribution . . . . . . . . . . . . . . . . . . . . 66 3.4.1 Discrete random variables . . . . . . . . . . . . . . . . . . . . . . . 66 3.4.2 Continuous random variables . . . . . . . . . . . . . . . . . . . . . 73Continuous random variables ....
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This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Pennsylvania State University, University Park.

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401txt - Statistics 401: An Introduction to Statistics for...

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