Lecture Guide and Student Notebook of MATH1131

# Lecture Guide and Student Notebook of MATH1131 - Lecture...

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Unformatted text preview: Lecture Guide and Student Notebook to accompany Introductory Statistics: A Problem Solving Approach Stephen M. Kokoska September 23, 2006 Contents 1 An Introduction to Statistics and Statistical Inference 1 1.1 Statistics Today . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Populations, Samples, Probability, and Statistics . . . . . . . . . . . . . . . . . 3 1.3 Experiments and Random Samples . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Tables and Graphs for Summarizing Data 13 2.1 Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Bar Charts and Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4 Frequency Distributions and Histograms . . . . . . . . . . . . . . . . . . . . . 31 3 Numerical Summary Measures 43 3.1 Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Measures of Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3 The Empirical Rule and Measures of Relative Standing . . . . . . . . . . . . . 60 3.4 Five-Number Summary and Box Plots . . . . . . . . . . . . . . . . . . . . . . 70 4 Probability 75 4.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.1 Experiments, Sample Spaces, and Events . . . . . . . . . . . . . . . . . . . . . 75 4.2 An Introduction to Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.3 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.5 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5 Random Variables and Discrete Probability Distributions 127 5.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.1 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 i ii 5.2 Probability Distributions for Discrete Random Variables . . . . . . . . . . . . 132 5.3 Mean, Variance, and Standard Deviation for a Discrete Random Variable . . . 139 5.4 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.5 Other Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6 Continuous Probability Distributions 167 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.2 Probability Distributions for a Continuous Random Variable . . . . . . . . . . 167 6.3 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 6.4 Checking the Normality Assumption . . . . . . . . . . . . . . . . . . . . . . . 191 6.5 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 7 Sampling Distributions 199 7.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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Lecture Guide and Student Notebook of MATH1131 - Lecture...

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