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1 Why probability and statistics? |
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1 | (12) |
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1.1 Biometry: iris recognition |
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1 | (2) |
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3 | (1) |
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1.3 Cars and goats: the Monty Hall dilemma |
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4 | (1) |
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1.4 The space shuttle Challenger |
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5 | (2) |
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1.5 Statistics versus intelligence agencies |
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7 | (2) |
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9 | (4) |
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2 Outcomes, events, and probability |
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13 | (12) |
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13 | (1) |
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14 | (2) |
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16 | (2) |
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2.4 Products of sample spaces |
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18 | (1) |
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2.5 An infinite sample space |
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19 | (2) |
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2.6 Solutions to the quick exercises |
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21 | (1) |
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21 | (4) |
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3 Conditional probability and independence |
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25 | (16) |
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3.1 Conditional probability |
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25 | (2) |
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3.2 The multiplication rule |
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27 | (3) |
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3.3 The law of total probability and Bayes' rule |
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30 | (2) |
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32 | (3) |
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3.5 Solutions to the quick exercises |
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35 | (2) |
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37 | (4) |
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4 Discrete random variables |
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41 | (16) |
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41 | (2) |
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4.2 The probability distribution of a discrete random variable |
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43 | (2) |
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4.3 The Bernoulli and binomial distributions |
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45 | (3) |
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4.4 The geometric distribution |
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48 | (2) |
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4.5 Solutions to the quick exercises |
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50 | (1) |
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51 | (6) |
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5 Continuous random variables |
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57 | (14) |
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5.1 Probability density functions |
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57 | (3) |
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5.2 The uniform distribution |
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60 | (1) |
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5.3 The exponential distribution |
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61 | (2) |
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5.4 The Pareto distribution |
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63 | (1) |
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5.5 The normal distribution |
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64 | (1) |
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65 | (2) |
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5.7 Solutions to the quick exercises |
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67 | (1) |
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68 | (3) |
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71 | (18) |
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71 | (1) |
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6.2 Generating realizations of random variables |
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72 | (3) |
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6.3 Comparing two jury rules |
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75 | (5) |
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6.4 The single-server queue |
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80 | (4) |
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6.5 Solutions to the quick exercises |
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84 | (1) |
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85 | (4) |
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7 Expectation and variance |
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89 | (14) |
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89 | (4) |
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93 | (1) |
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7.3 The change-of-variable formula |
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94 | (2) |
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96 | (3) |
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7.5 Solutions to the quick exercises |
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99 | (1) |
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99 | (4) |
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8 Computations with random variables |
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103 | (12) |
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8.1 Transforming discrete random variables |
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103 | (1) |
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8.2 Transforming continuous random variables |
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104 | (2) |
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106 | (2) |
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108 | (2) |
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8.5 Solutions to the quick exercises |
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110 | (1) |
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111 | (4) |
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9 Joint distributions and independence |
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115 | (20) |
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9.1 Joint distributions of discrete random variables |
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115 | (3) |
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9.2 Joint distributions of continuous random variables |
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118 | (4) |
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9.3 More than two random variables |
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122 | (2) |
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9.4 Independent random variables |
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124 | (1) |
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9.5 Propagation of independence |
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125 | (1) |
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9.6 Solutions to the quick exercises |
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126 | (1) |
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127 | (8) |
10 Covariance and correlation |
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135 | (16) |
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10.1 Expectation and joint distributions |
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135 | (3) |
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138 | (3) |
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10.3 The correlation coefficient |
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141 | (2) |
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10.4 Solutions to the quick exercises |
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143 | (1) |
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144 | (7) |
11 More computations with more random variables |
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151 | (16) |
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11.1 Sums of discrete random variables |
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151 | (3) |
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11.2 Sums of continuous random variables |
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154 | (5) |
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11.3 Product and quotient of two random variables |
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159 | (3) |
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11.4 Solutions to the quick exercises |
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162 | (1) |
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163 | (4) |
12 The Poisson process |
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167 | (14) |
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167 | (1) |
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12.2 Taking a closer look at random arrivals |
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168 | (3) |
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12.3 The one-dimensional Poisson process |
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171 | (2) |
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12.4 Higher-dimensional Poisson processes |
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173 | (3) |
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12.5 Solutions to the quick exercises |
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176 | (1) |
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176 | (5) |
13 The law of large numbers |
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181 | (14) |
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181 | (2) |
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13.2 Chebyshev's inequality |
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183 | (2) |
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13.3 The law of large numbers |
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185 | (3) |
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13.4 Consequences of the law of large numbers |
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188 | (3) |
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13.5 Solutions to the quick exercises |
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191 | (1) |
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191 | (4) |
14 The central limit theorem |
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195 | (12) |
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14.1 Standardizing averages |
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195 | (4) |
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14.2 Applications of the central limit theorem |
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199 | (3) |
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14.3 Solutions to the quick exercises |
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202 | (1) |
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203 | (4) |
15 Exploratory data analysis: graphical summaries |
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207 | (24) |
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15.1 Example: the Old Faithful data |
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207 | (2) |
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209 | (3) |
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15.3 Kernel density estimates |
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212 | (7) |
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15.4 The empirical distribution function |
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219 | (2) |
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221 | (4) |
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15.6 Solutions to the quick exercises |
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225 | (1) |
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226 | (5) |
16 Exploratory data analysis: numerical summaries |
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231 | (14) |
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16.1 The center of a dataset |
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231 | (2) |
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16.2 The amount of variability of a dataset |
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233 | (1) |
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16.3 Empirical quantiles, quartiles, and the IQR |
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234 | (2) |
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16.4 The box-and-whisker plot |
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236 | (2) |
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16.5 Solutions to the quick exercises |
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238 | (2) |
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240 | (5) |
17 Basic statistical models |
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245 | (24) |
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17.1 Random samples and statistical models |
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245 | (3) |
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17.2 Distribution features and sample statistics |
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248 | (5) |
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17.3 Estimating features of the "true" distribution |
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253 | (3) |
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17.4 The linear regression model |
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256 | (3) |
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17.5 Solutions to the quick exercises |
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259 | (1) |
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259 | (10) |
18 The bootstrap |
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269 | (16) |
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18.1 The bootstrap principle |
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269 | (3) |
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18.2 The empirical bootstrap |
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272 | (4) |
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18.3 The parametric bootstrap |
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276 | (3) |
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18.4 Solutions to the quick exercises |
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279 | (1) |
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280 | (5) |
19 Unbiased estimators |
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285 | (14) |
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285 | (2) |
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19.2 Investigating the behavior of an estimator |
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287 | (1) |
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19.3 The sampling distribution and unbiasedness |
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288 | (4) |
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19.4 Unbiased estimators for expectation and variance |
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292 | (2) |
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19.5 Solutions to the quick exercises |
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294 | (1) |
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294 | (5) |
20 Efficiency and mean squared error |
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299 | (14) |
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20.1 Estimating the number of German tanks |
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299 | (3) |
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20.2 Variance of an estimator |
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302 | (3) |
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305 | (2) |
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20.4 Solutions to the quick exercises |
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307 | (1) |
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307 | (6) |
21 Maximum likelihood |
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313 | (16) |
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21.1 Why a general principle? |
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313 | (1) |
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21.2 The maximum likelihood principle |
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314 | (2) |
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21.3 Likelihood and loglikelihood |
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316 | (5) |
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21.4 Properties of maximum likelihood estimators |
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321 | (1) |
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21.5 Solutions to the quick exercises |
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322 | (1) |
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323 | (6) |
22 The method of least squares |
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329 | (12) |
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22.1 Least squares estimation and regression |
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329 | (3) |
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332 | (3) |
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22.3 Relation with maximum likelihood |
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335 | (1) |
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22.4 Solutions to the quick exercises |
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336 | (1) |
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337 | (4) |
23 Confidence intervals for the mean |
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341 | (20) |
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341 | (4) |
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345 | (5) |
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23.3 Bootstrap confidence intervals |
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350 | (3) |
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353 | (2) |
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23.5 Solutions to the quick exercises |
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355 | (1) |
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356 | (5) |
24 More on confidence intervals |
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361 | (12) |
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24.1 The probability of success |
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361 | (3) |
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24.2 Is there a general method? |
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364 | (2) |
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24.3 One-sided confidence intervals |
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366 | (1) |
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24.4 Determining the sample size |
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367 | (1) |
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24.5 Solutions to the quick exercises |
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368 | (1) |
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369 | (4) |
25 Testing hypotheses: essentials |
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373 | (10) |
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25.1 Null hypothesis and test statistic |
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373 | (3) |
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376 | (1) |
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25.3 Type I and type II errors |
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377 | (2) |
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25.4 Solutions to the quick exercises |
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379 | (1) |
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380 | (3) |
26 Testing hypotheses: elaboration |
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383 | (16) |
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383 | (3) |
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26.2 Critical region and critical values |
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386 | (4) |
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390 | (2) |
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26.4 Relation with confidence intervals |
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392 | (1) |
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26.5 Solutions to the quick exercises |
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393 | (1) |
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394 | (5) |
27 The t-test |
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399 | (16) |
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27.1 Monitoring the production of ball bearings |
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399 | (2) |
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27.2 The one-sample t-test |
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401 | (4) |
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27.3 The t-test in a regression setting |
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405 | (4) |
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27.4 Solutions to the quick exercises |
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409 | (1) |
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410 | (5) |
28 Comparing two samples |
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415 | (14) |
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28.1 Is dry drilling faster than wet drilling? |
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415 | (1) |
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28.2 Two samples with equal variances |
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416 | (3) |
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28.3 Two samples with unequal variances |
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419 | (3) |
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422 | (2) |
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28.5 Solutions to the quick exercises |
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424 | (1) |
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424 | (5) |
A Summary of distributions |
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429 | (2) |
B Tables of the normal and t-distributions |
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431 | (4) |
C Answers to selected exercises |
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435 | (10) |
D Full solutions to selected exercises |
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445 | (30) |
References |
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475 | (2) |
List of symbols |
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477 | (2) |
Index |
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479 | |