List of Figures

3.1 Log(Frequency) vs. Log(Rank) for the words in Dickens’s A ChristmasCarol.

4.1 Plot of the running estimate of the probability of heads for 50 flips.

4.2 Plot of the running estimate of the probability of heads for 5000 flips.

4.3 Histogram of the proportions of the letter e in 68 Poe short stories based ontable4.l.

4.4 Histogram and best fitting normal curve for the proportions of the letter e in 68 Poe short stories.

4.5 Plot of the number of types versus the number of tokens for “The Unparalleled Adventures of One Hans Pfaall.” Data is from program 4.5.Figure adapted from figure 1.1 of Baayen [61 with kind permission from Springer Science and Business Media and the author.

4.6 Plot of the mean word frequency against the number of tokens for “The Unparalleled Adventures of One Hans Pfaall.” Data is from program 4.5. Figure adapted from figure 1.1 of Baayen [61] with kind permission from Springer Science and Business Media and the author.

4.7 Plot of the mean word frequency against the number of tokens for “The Unparalleled Adventures of One Hans Pfaall” and “The Black Cat.” Figure adapted from figure 1.1 of Baayen [6] with kind permission from Springer Science and Business Media and the author.

5.1 The vector (4,3) makes a right triangle if a line segment perpendicular to the x-axis is drawn to the x-axis.

5.2 Comparing the frequencies of the word the (on the x-axis) against city (on the y-axis). Note that the y-axis is not to scale: it should be more compressed.

5.3 Comparing the logarithms of the frequencies for the words the (on the x-axis) and city (on the y-axis).

7.1 Plotting pairs of word counts for the 68 Poe short stories.

7.2 Plots of the word counts for the versus of using the 68 Poe short stories.

8.1 A two variable data set that has two obvious clusters.

8.2 The perpendicular bisector of the line segment from (0,1) to (1,1)divides this plot into two half-planes. The points in each form the two clusters.

8.3 The next iteration of k-means after figure 8.2. The line splits the data into two groups, and the two centroids are given by the asterisks.

8.4 Scatterplot of heRate against sheRate for Poe’s 68 short stories.

8.5 Plot of two short story clusters fitted to the heRate and sheRate data.

8.6 Plots of three, four, five, and six short story clusters fitted to the heRate and sheRate data.

8.7 Plots of two short story clusters based on eight variables, but only plotted for the two variables heRate and sheRate.

8.8 Four more plots showing projections of the two short story clusters found in output 8.7 onto two pronoun rate axes.

8.9 Eight principal components split into two short story clusters and projected onto the first two PCs.

8.10 A portion of the dendrogram computed in output 8.11, which shows hierarchical clusters for Poe’s 68 short stories.

8.11 The plot of the Voronoi diagram computed in output 8.12.

8.12 All four plots have uniform marginal distributions for both the x and y-axes. For problem 8.4.

8.13 The dendrogram for the distances between pronouns based on Poe’s 68 short stories. For problem 8.5.

9.1 Histogram of the numbers of runs in 100,000 random permutations of digits in equation 9.1.

9.2 Histogram of the runs of the 10,000 permutations of the names Scrooge and Marley as they appear in A Christmas Carol.

9.3 Histogram of the runs of the 10,000 permutations of the names Francois and Perrault as they appear in The Call of the Wild.