Section | Page | Type | Title |

Preface | xvi | Graph | Historical Timeline |

1.8 | 14 | Full Program | Simple R program |

15 | Fragment | Ending an R session |

15 | Full Program | Defining a sequence of numbers |

15 | Full Program | Defining a sequence of squares |

15 | Fragment | Obtaining documentation for a function |

16 | Full Program | Applying a function to a vector |

16 | Full Program | The base 10 logarithm function |

16 | Full Program | Defining a vector |

16 | Full Program | Defining a vector with other vectors |

16 | Full Program | Extracting one element of a vector |

16 | Full Program | Tossing a fair coin 10 times |

17 | Full Program | Comparing a vector to a number |

17 | Full Program | Finding the heads in a vector of fair coin tosses |

17 | Fragment | Assigning a name to an vector |

17 | Fragment | Another way to assign a name to a vector |

18 | Fragment | Finding the heads in a vector of biased coin tosses |

18 | Full Program | Invoking a function |

18 | Full Program | Adding a vector to a number |

18 | Full Program | Adding a vector to a vector |

1.10 | 27 | Full Program | Rolling a die to get a 6 |

28 | Full Program | Adding the integers from 1 to 100 |

28 | Full Program | Adding the first 100 squares |

28 | Full Program | The numbers from -6 to 6 in increments of 0.001 |

28 | Full Program | Another way to compute the numbers from -6 to 6 in increments of 0.001 |

2.3 | 32 | Full Program | Logarithm of the factorial |

33 | Full Program | Factorial logarithm base 10 |

2.5 | 36 | Fragment | Probability for a birthday coincidence |

36 | Full Program | Probabilities for a birthday coincidence using logarithms |

37 | Graph | The probabilities for birthday coincidences |

38 | Full Program | Probability for selecting a random committee |

38 | Full Program | Another model for random committee selection |

2.7 | 42 | Full Program | Smuggler probability problem |

42 | Full Program | Probability for winning in the game of Craps |

43 | Full Program | Poker probabilities |

44 | Full Program | Chinese dice game probabilities |

45 | Graph | The probabilities for catching tagged fish |

45 | Full Program | Computing the maximum likelihood estimation |

46 | Fragment | Probability for horoscope coincidence |

46 | Full Program | Probability for horoscope coincidence using logarithms. |

3.1 | 50 | Full Program | The waiting time for a head in the Bernoulli process |

50 | Full Program | A function for computing the Bernoulli process waiting time |

50 | Full Program | Computing a sequence of Bernoulli process waiting times |

50 | Graph | Tabulation of Bernoulli waiting times |

51 | Graph | Another way to tabulate and graph Bernoulli waiting times |

52 | Fragment | The geometric distribution for various biases |

52 | Graph | Grouping R commands |

53 | Full Program | Waiting times in the Bernoulli process |

53 | Full Program | The waiting time for the third head in the Bernoulli process |

53 | Full Program | Unknown values |

54 | Graph | Tabulation of waiting times in the Bernoulli process |

54 | Graph | The negative binomial distribution for various biases |

55 | Graph | Various negative binomial distributions for a fair coin |

57 | Graph | A binomial distribution |

58 | Animation | Animation of the binomial distribution for biases from 0 to 1 |

58 | Animation | Animation of the binomial distribution for biases from 0 to 1 with specified vertical scale |

59 | Animation | Animation of the binomial distribution for 1 to 100 trials |

59 | Animation | Animation of the binomial distribution for 1 to 200 trials with specified vertical scale |

59 | Animation | Animation of the binomial distribution for bias 0.25 |

60 | Fragment | Vectors used for computing the gaps in the Bernoulli process |

3.2 | | Graph | Random walk for a specific Bernoulli sample point |

61 | Animation | Animation of a random walk |

3.7 | 76 | Graph | Playing card scores |

77-78 | Graph | The distribution of a biased random walk |

78 | Fragment | Computing the most likely location for a biased random walk |

78 | Graph | A function for computing the most likely location for a biased random walk |

79 | Animation | Animation of a biased random walk |

| Animation | Observing the movement of the most likely location for a biased random walk |

79 | Animation | Animation of a biased random walk with fixed limits |

| Animation | Animation of a biased random walk with fixed limits, showing the most likely location |

80 | Full Program | Expected score of a randomly chosen card |

80 | Full Program | Expected score of a randomly chosen card |

82 | Graph | The birthday coincidence waiting time distribution |

83 | Full Program | Specific example of the waiting time for a birthday coincidence |

83 | Full Program | Specific example of the waiting time for a birthday coincidence |

83 | Full Program | Expected waiting time for a birthday coincidence |

85 | Graph | The Banach matchbox probabilities |

85 | Full Program | Two ways to compute the expectation for the Banach matchbox problem |

4.0 | 88 | Graph | Distribution of a uniform random variable |

| Graph | Density function of a uniform random variable |

90 | Graph | Graph symbols available in R |

4.1 | 91 | Fragment | Computing the first order statistic |

91 | Fragment | Computing the third order statistic |

91 | Graph | The distribution of the first order statistic (i.e., the minimum) |

92 | Graph | The density of the first order statistic |

4.2 | 93 | Graph | Distribution of a typical integer random variable |

4.9 | 111-112 | Graph | Comparison of X(1) and log(X(1)), graph is on page 112 |

113 | Graph | Trapezoidal region for computing the distribution function of the spread |

116-117 | Graph | The distribution of the smallest piece of broken DNA molecule |

117 | Full Program | Confidence interval for the smallest piece of a broken DNA molecule |

117 | Full Program | Confidence interval for the smallest piece of a broken DNA molecule |

118 | Full Program | Expected number of cards one must observe until one sees a spade |

5.1 | 123 | Graph | Variance of a Bernoulli trial as a function of the bias |

| Graph | Standard deviation of a Bernoulli trial |

5.2 | | Graph | Standard normal density function |

| Graph | Standard normal distribution function |

| Graph | Inverse of the standard normal distribution function |

5.3 | 129 | Graph | Comparison of a Binomial density with the corresponding normal density |

| Graph | Comparison of S(16) with N(8,4) |

130 | Graph | Various normal distributions with mean 0 |

5.4 | 132 | Full Program | Significance of a test for the unfairness of a coin |

133 | Full Program | Significance of a test for whether a die is loaded |

134 | Full Program | Test of significance for whether a die is loaded |

5.5 | 134 | Full Program | Confidence interval for accommodating airplane passengers |

135 | Full Program | Another confidence interval for accommodating airplane passengers |

135 | Full Program | Normal approximation to confidence intervals |

5.7 | 140-141 | Graph | Randomly generated tennis ball hits |

141-142 | Graph | Random generation using the Cauchy distribution function |

142 | Animation | Animation of the Cauchy distribution and its mean value |

5.9 | 158 | Full Program | A one-sided significance test of a hypothesis |

158 | Full Program | A two-sided significance test of whether a sample is random |

158 | Full Program | A one-sided significance test of whether a sample is random |

159 | Graph | Normal model of significance for a manufacturing process |

160 | Full Program | Test of significant effect for an advertising campaign |

160 | Full Program | Test of significant effect for a public relations campaign |

161 | Full Program | Test whether a questionnaire was badly worded |

161 | Full Program | Retest of significance for a public relations campaign |

162 | Full Program | How often a professor has coffee before class |

162 | Full Program | Resource provisioning for a telephone company |

163 | Full Program | Resource provisioning alternative for a telephone company |

163 | Full Program | Salary comparisons for men and women |

163 | Full Program | Test whether an experiment was properly performed |

6.7 | 188 | Full Program | Example of rejection sampling |

6.9 | 200 | Full Program | The effect of information on probabilities |

7.1 | 210 | Graph | Various exponential distributions |

211 | Graph | Various exponential densities |

7.2 | 215 | Full Program | Extracting the times when heads occur in a Bernoulli sample point |

7.6 | 237 | Full Program | Probability of exactly 4 misprints on a page in a textbook: Bernoulli model |

237 | Full Program | Probability of at least 4 misprints on a page in a textbook: Bernoulli model |

237 | Full Program | Probability of 4 misprints on a page in a textbook: Poisson model |

238 | Full Program | Probability of 8 misprints on a page in a textbook |

239 | Full Program | Probability of 4 misprints on any page in a textbook |

239 | Full Program | Probability of 8 misprints on any page in a textbook |

239 | Full Program | Statistical significance of an all-white class |

240 | Full Program | Confidence interval for an inventory problem |

240 | Full Program | Probabilities in a criminal case |

8.4 | | Graph | Conditional density of a renewal time |

8.7 | 255 | Animation | Animation of the evolution of a randomized Bernoulli process |

| Animation | Evolution of a randomized Bernoulli process with varying scale |

255 | Animation | Animation comparing Bayesian reasoning with a normal approximation |

8.8 | 257 | Graph | Probability distribution of the time until failure |

258 | Graph | Probability density of the time until failure |

| Graph | An example of a reliability comparison using densities of the time until failure |

8.9 | 259 | Randomization Program | Randomization program for defining a randomized Poisson process |

259 | Randomization Program | Randomization program for defining a compound process |

260 | Randomization Program | Randomization program for defining a Poisson process randomized by a normal process |

8.11 | 270 | Full Program | Confidence interval for the time until a crystal is fully covered |

272 | Graph | Some reliability distributions |

273 | Graph | Some reliability densities |

9.1 | 278 | Graph | Entropy of a Bernoulli trial |

279 | Graph | Comparison of linear and logarithmic functions |

10.1 | 305 | Randomization Program | Randomization program for defining a Markov chain as a stochastic process |

306 | Randomization Program | Randomization program for defining a Markov chain as a stochastic process |

10.4 | 314 | Animation | Animation for the gambler's ruin |

| Animation | Animation for the gambler's ruin, with varying vertical scale |

| Animation | Animation for a random walk with reflecting barriers |

| Animation | Animation for a random walk with reflecting barriers and varying vertical scale |

10.9 | 333 | Fragment | Invariant distribution for taking exams |

334 | Full Program | Tournament strategies |

A.1 | 343 | Graph | The reflection principle for the arcsine law: Diagram #1 |

344 | Graph | The reflection principle for the arcsine law: Diagram #2 |

345 | Graph | The reflection principle for the arcsine law: Diagram #3 |

| Graph | Typical random walk for the event C[n,a,x]-C[n,a+1,x] of the reflection principle |

A.2 | 347 | Graph | The reflection principle for the arcsine law: Diagram #4 |

| | Graph | Wiener process |