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in human DNA.TABLE 3.4. Deaths by horse kicks in the Prussian cavalry.TABLE 3.5. Bomb hits over London during World War II.TABLE 3.6. No-hitter baseball games

      4 Chapter 4TABLE 4.1. Discrete probability distributions.TABLE 4.2. Tile values in Scrabble.TABLE 4.3. Distribution of US households by number of TVs.TABLE 4.4. Fixed points of permutations for

.TABLE 4.5. Household size by vehicles available.

      5 Chapter 5TABLE 5.1. Lengths of 112 World Series, 1903–2019.TABLE 5.2. Distribution of colors in a bag of candies.TABLE 5.3. Genotype frequencies for a sample of 60 fruit flies.TABLE 5.4. Benford's law.

      6 Chapter 7TABLE 7.1. Comparison of tail probabilities for normal and Pareto distributions...TABLE 7.2. SAT statistics for 2011 college-bound seniors

      7 Chapter 10TABLE 10.1. Grade distribution for AP examsTABLE 10.2. Monte Carlo approximation of the mean of a uniform distribution. Co...

      8 Chapter 11TABLE 11.1. Simple random walk for the cycle graph on nine vertices after steps...

      9 Appendix ATABLE A.1. Probability distributions in R.

      List of Illustrations

      1 IntroductionFIGURE I.1: Benford's law describes the frequencies of first digits for many...

      2 Chapter 1FIGURE 1.1: Venn diagrams.FIGURE 1.2: Venn diagram.FIGURE 1.3: Pascal's triangle.FIGURE 1.4: Illustrating the correspondence between “bad” lists that start w...FIGURE 1.5: Venn diagram.

      3 Chapter 2FIGURE 2.1: FIGURE 2.2: Tree diagram for picking two balls from a bag of two red and thr...FIGURE 2.3: Tree diagram for Example 2.7.FIGURE 2.4: Tree diagram for blackjack.FIGURE 2.5: Solving the birthday problem with a tree diagram.FIGURE 2.6: The events

partition the sample space. The circle represents e...FIGURE 2.7: Nontransitive dice.

      4 Chapter 3FIGURE 3.1: Four examples of the binomial distribution.FIGURE 3.2: Three random graphs on

vertices generated, respectively, with FIGURE 3.3: Four Poisson distributions with varying

.

      5 Chapter 4FIGURE 4.1: Four distributions with

. Variances are (a) 0, (b) 2.08, (c) 4,...FIGURE 4.2: Simulation of Poisson(25) distribution. Vertical lines are drawn...FIGURE 4.3: Covariance is a measure of linear association between two random...FIGURE 4.4: Randomly colored six-by-six board. There are 19 one-by-one black...

      6 Chapter 5FIGURE 5.1: Graph of

.

      7 Chapter 6FIGURE 6.1: Density with shaded area indicating

.FIGURE 6.2: Three density shapes.FIGURE 6.3: Density function and cdf.FIGURE 6.4: Cumulative distribution function

for

The cdf has points of d...FIGURE 6.5: Zoe arrives at the bus station 10 minutes after Adrian. But the ...FIGURE 6.6: Bathtub curves are used in reliability engineering to model fail...FIGURE 6.7: Joint density

FIGURE 6.8: Shaded region defined by

FIGURE 6.9: (a) Joint density

. (b) Domain of joint density. Shaded region ...FIGURE 6.10: (a) Joint density. (b) Shaded region shows event

in the part ...FIGURE 6.11: Accept–reject method for simulating points uniformly distribute...FIGURE 6.12: One thousand points generated in the unit sphere using the acce...

      8 Chapter 7FIGURE 7.1: Three normal distributions.FIGURE 7.2: Normal approximation of the binomial distribution. For fixed

, ...FIGURE 7.3: Approximating the binomial probability

using a normal distribu...FIGURE 7.4: Four gamma distributions.FIGURE 7.5: The histogram is from simulating the sum of 20 exponential varia...FIGURE 7.6: Poisson process: relationships of underlying random variables.FIGURE 7.7: Four beta distributions.FIGURE 7.8: Scale-invariance of the Pareto distribution. The density curve i...

      9 Chapter 8FIGURE 8.1: Simulated distribution of

, where

The curve is the density fu...FIGURE 8.2: The geometry of the lighthouse problem.FIGURE 8.3: Simulating from density

using the inverse transform method.FIGURE 8.4: Simulated distribution of three independent exponential random v...FIGURE 8.5: Distributions from (a) to (c): uniform, sum of two independent u...FIGURE 8.6: The shaded region is the event that Angel and Lisa meet.FIGURE 8.7: Let

be uniformly distributed on the triangle. The shaded regio...FIGURE 8.8: Region

for

and

.FIGURE 8.9: Geometry of Buffon's needle problem. The needle intersects a lin...FIGURE 8.10: Buffon's needle problem is solved by finding the area under the...

      10 Chapter 9FIGURE 9.1: (a) Graph of a joint density function. (b) Conditional density o...FIGURE 9.2: Graph of conditional density of

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