1 Descriptive statistics . 11 1.1 Population and samples . 11 1.2 The median . 15 1.3 Quartiles and mode . 16 1.

4 Relative frequency and histograms . 18 1.5 The mean . 19 1.6 Sample variance and sample standard deviation . 21 1.7 Sample covariance and coefficient of variation . 23 1.

8 Using Excel . 26 1.9 Summary of Chapter 1 . 28 1.10 Problems for chapter 1 . 30 2 Probability . 37 2.1 Sample space .

37 2.2 Probability . 38 2.2.1 Events . 39 2.2.2 Uniform probability .

40 2.2.3 Set theory . 41 2.2.4 Computing probabilities . 43 2.2.

5 The negation principle . 45 2.3 Summary of Chapter 2 . 45 2.4 Problems for chapter 2 . 45 3 Combinatorics . 51 3.1 Counting combinations .

51 3.1.1 Ordered selections . 52 3.1.2 Unordered choices without replacement . 54 3.1.

3 Combinatorial probabilities . 57 3.2 Summary of Chapter 3 . 59 3.3 Problems for chapter 3 . 59 4 Conditional probability . 65 4.1 Conditional probability .

65 4.1.1 Computing conditional probabilities . 67 4.1.2 Splitting the sample space . 69 4.1.

3 Probability trees . 69 4.2 Subjective probabilities . 74 4.3 Independence . 75 4.4 Summary of Chapter 4 . 76 4.

5 Problems for chapter 4 . 77 5 Random variables, mean and variance . 87 5.1 Random variables . 87 5.2 Expectation . 91 5.2.

1 Computing expectations . 93 5.2.2 General expectations and variance . 94 5.3 Some simple facts about option pricing . 96 5.3.

1 Hedging portfolios . 97 5.4 Summary of Chapter 5 . 99 5.5 Problems for chapter 5 . 100 6 Joint distributions . 109 6.1 Simultaneous distributions .

109 6.2 Covariance . 114 6.2.1 An alternative formula for the covariance . 115 6.2.2 Sums of random variables .

116 6.3 Summary of Chapter 6 . 117 6.4 Problems for chapter 6 . 118 7 Basic probability distributions . 125 7.1 The indicator distribution . 125 7.

2 The binomial distribution . 126 7.3 The hypergeometric distribution . 129 7.4 The Poisson distribution . 133 7.5 The normal distribution . 135 7.

5.1 The general normal distribution . 138 7.5.2 Standardizing random variables . 139 7.5.3 The central limit theorem .

140 7.5.4 Integer correction . 145 7.5.5 Normal approximation of hypergeometric and Poisson distributions . 147 7.5.

6 Summing normal distributions . 148 7.5.7 Applications to option pricing . 148 7.6 Summary of chapter 7 . 150 7.7 Problems for chapter 7 .

152 8 Estimation . 169 8.1 Estimation . 169 8.1.1 Estimators . 170 8.1.

2 Reporting estimates . 172 8.1.3 The measurement model . 172 8.2 Confidence intervals . 173 8.2.

1 Constructing confidence intervals . 174 8.2.2 The t-distribution . 176 8.3 The lottery model . 179 8.4 Summary of Chapter 8 .

180 8.5 Problems for chapter 8 . 181 9 Hypothesis testing . 185 9.1 Basic ideas . 185 9.2 Motivation . 187 9.

3 General principles for hypothesis testing . 189 9.4 Designing statical tests . 191 9.4.1 One-sided and two-sided tests . 195 9.4.

2 Confidence intervals and hypothesis testing . 196 9.4.3 P-value . 197 9.5 Summary of Chapter 9 .