section2.2

# section2.2 - Contents I Probability 5 1 Sets and...

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Unformatted text preview: Contents I Probability 5 1 Sets and Probability 7 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . 8 1.1.2 Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . 14 1.1.3 Proportions . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . 34 1.3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.3.1 Random Experiments, Sample Spaces and Events . . . 59 1.3.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . 65 1.4 Conditional Proportions and Probabilities . . . . . . . . . . . 84 1.4.1 Conditional Proportions . . . . . . . . . . . . . . . . . 84 1.4.2 Conditional Probabilities . . . . . . . . . . . . . . . . 87 1.4.3 Multiplicative Rule . . . . . . . . . . . . . . . . . . . . 91 1.4.4 Independence . . . . . . . . . . . . . . . . . . . . . . . 92 1.5 Compound Experiments . . . . . . . . . . . . . . . . . . . . . 107 1.5.1 Finding Probabilities and Conditional Probabilities in Compound Experiments . . . . . . . . . . . . . . . . . 108 1.5.2 Notation for Events in Compound Experiments . . . . 117 1.5.3 Using the Multiplicative Rule to Find Probabilities in Compound Experiments . . . . . . . . . . . . . . . . . 119 1.5.4 More Examples . . . . . . . . . . . . . . . . . . . . . . 124 1.6 Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 145 2 Variables 163 2.1 Variables and their Distributions . . . . . . . . . . . . . . . . 164 2.1.1 Basic Definitions of Variables and Random Variables . 164 2.1.2 Classifying Variables . . . . . . . . . . . . . . . . . . . 168 2.1.3 Distributions of Variables and Random Variables . . . 169 1 2 CONTENTS 2.1.4 Distributions of Categorical Variables . . . . . . . . . 170 2.1.5 Distributions of Numerical Discrete Variables . . . . . 175 2.1.6 Distributions of Numerical Continuous Variables . . . 180 2.1.7 Experimental Distributions . . . . . . . . . . . . . . . 191 2.2 Percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 2.3 Mean and Standard Deviation . . . . . . . . . . . . . . . . . . 201 2.3.1 The Mean . . . . . . . . . . . . . . . . . . . . . . . . . 201 2.3.2 Variance and Standard Deviation . . . . . . . . . . . . 210 2.4 Joint Distributions . . . . . . . . . . . . . . . . . . . . . . . . 225 2.5 Association Between Variables . . . . . . . . . . . . . . . . . 242 2.5.1 Conditional Distributions . . . . . . . . . . . . . . . . 242 2.5.2 Independence . . . . . . . . . . . . . . . . . . . . . . . 246 2.5.3 Observing Association in Scatterplots . . . . . . . . . 249 2.5.4 Covariance . . . . . . . . . . . . . . . . . . . . . . . . 253 2.5.5 Correlation . . . . . . . . . . . . . . . . . . . . . . . . 257 2.5.6 Properties of Correlation . . . . . . . . . . . . . . . . 263 2.6 Combining Variables . . . . . . . . . . . . . . . . . . . . . . . 277 2.6.1 Y = f ( X ) . . . . . . . . . . . . . . . . . . . . . . . . . 277) ....
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section2.2 - Contents I Probability 5 1 Sets and...

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