“mcs”-2018/6/6一13：43一page vii一#7 vii Contents IV Probability Introduction 771 17 Events and Probability Spaces 773 17.1 Let's Make a Deal 773 17.2 The Four Step Method 774 17.3 Strange Dice 783 17.4 The Birthday Principle 790 17.5 Set Theory and Probability 792 17.6 References 796 18 Conditional Probability 805 18.1 Monty Hall Confusion 805 18.2 Definition and Notation 806 18.3 The Four-Step Method for Conditional Probability 808 18.4 Why Tree Diagrams Work 810 18.5 The Law of Total Probability 818 18.6 Simpson's Paradox 820 18.7 Independence 822 18.8 Mutual Independence 824 18.9 Probability versus Confidence 828 19 Random Variables 857 19.1 Random Variable Examples 857 19.2 Independence 859 19.3 Distribution Functions 861 19.4 Great Expectations 869 19.5 Linearity of Expectation 881 19.6 Really Great Expectations 890 20 Deviation from the Mean 915 20.1 Markov's Theorem 915 20.2 Chebyshev's Theorem 918 20.3 Properties of Variance 922 20.4 Estimation by Random Sampling 928 20.5 Sums of Random Variables 933 21 Random Walks 965 21.1 Gambler's Ruin 965 21.2 Random Walks on Graphs 975“mcs” — 2018/6/6 — 13:43 — page vii — #7 Contentsvii IV Probability Introduction 771 17 Events and Probability Spaces 773 17.1 Let’s Make a Deal 773 17.2 The Four Step Method 774 17.3 Strange Dice 783 17.4 The Birthday Principle 790 17.5 Set Theory and Probability 792 17.6 References 796 18 Conditional Probability 805 18.1 Monty Hall Confusion 805 18.2 Definition and Notation 806 18.3 The Four-Step Method for Conditional Probability 808 18.4 Why Tree Diagrams Work 810 18.5 The Law of Total Probability 818 18.6 Simpson’s Paradox 820 18.7 Independence 822 18.8 Mutual Independence 824 18.9 Probability versus Confidence 828 19 Random Variables 857 19.1 Random Variable Examples 857 19.2 Independence 859 19.3 Distribution Functions 861 19.4 Great Expectations 869 19.5 Linearity of Expectation 881 19.6 Really Great Expectations 890 20 Deviation from the Mean 915 20.1 Markov’s Theorem 915 20.2 Chebyshev’s Theorem 918 20.3 Properties of Variance 922 20.4 Estimation by Random Sampling 928 20.5 Sums of Random Variables 933 21 Random Walks 965 21.1 Gambler’s Ruin 965 21.2 Random Walks on Graphs 975