Index

ballot theorem, 147–150

Bayes, Thomas, 122

Benford, Gregory, 188

Bernoulli, James, 28n9, 33–34, 52, 209

Bertrand, Joseph, 148

binomial: coefficient, 37, 43; theorem, 143, 145

Brams, Steven, 188

Cardano, Gerolamo, 1, 27n1

Carroll, Lewis. See Dodgson, Charles

conditional probability, 49, 118–125, 141

d’Alembert, Jean, 179–180

Davis, Matt, 26

de Méré, Chevalier, 1–4, 27n1

de Moivre, Abraham, 6, 8–10, 13, 16

density function, 110–111, 128, 140, 154, 196, 210

difference equation, 19, 25–26, 28n6, 157–159, 161, 165–166, 203–204

Dirichlet, Lejeune, 131

distribution function, 108–109, 111, 128, 140, 142, 154

Dodgson, Charles, 178–179

dominant decision strategy, 184, 186

Dresher, Melvin, 183

Durinx, Michel, 47, 50

Euler’s constant, 92

expected utility, 186–187

exponential (probability law), 139–141

false negative (positive), 117–119

Fermat, Pierre de, 2, 5–6

Flood, Merill, 183

floor (MATLAB^® command), 21

Fontana, Niccolo, 5

Galilei, Galileo, 3–4, 14

gambler’s ruin problem, 5–13, 28n9

Gardner, Martin, 185, 188

Gauss, Carl, 97

geometric probability, 63, 190, 192

Gombaud, Antoine. See de Méré, Chevalier

Goudsmit, Samuel, 25, 29n14

Groves, Leslie, 29n14

harmonic series, 29, 91

Hein, Piet, 188

Henderson, Shane, 48–51

Hobson, Nick, 43–44

Huygens, Christiaan, 6

hypothesis testing, 85–86

indicator function, 48

integral: differentiation of, 99; equation, 171

joint probability: in density, 98, 111–112, 210; in distribution, 112–114

Laplace, Pierre-Simon, 122–124

life expectancy table, 168, 172–173

Markov, Andrei, 157

max (MATLAB^® command), 152

maximum function, 108–109, 142, 154

memoryless property, 140–141, 148. See also exponential (probability law)

minimum function, 108–110, 142, 145

Monte Carlo, 213–216

Newcomb, William, 184–185, 188

Newton, Isaac, 6, 13–18, 28n9, 29n11, 54

Newton-Raphson method, 101

normally distributed (random variable), 96

Nozick, Robert, 185, 187

Pascal, Blaise de, 1–2, 5–7, 27n1

Pepys, Samuel, 13–16, 18, 29nn11, 12

perms (MATLAB^® command), 76

polar coordinates, 98

prisoner’s dilemma, 183–185

quad (MATLAB^® command), 101

random number generator, 213–216

rejection method, 199

Saiz, Steve, 47–49, 51

sample space, 3, 63, 120, 189–190, 192–194

Simpson, Edward, 22

Simpson, Thomas, 173

solve (MATLAB^® command), 71

standard deviation, 97

state-transition matrix, 157–158, 161–162

Steinhaus, Hugo, 17

Stirling’s formula, 41

subroutine, 205

Tartaglia. See Fontana, Niccolo

Taylor, Bruce, 42–43

Todhunter, Isaac, 179

total probability (theorem of), 120, 125n1

transitivity: in bingo cards, 75–78; in dice, 17–18

triangular inequality, 189, 191–193, 195

Trybuła, Stanislaw, 17

Tucker, Albert, 183

Viviani, Vincenzo, 30

vos Savant, Marilyn, 175–176, 180, 181n1

Whitworth, William, 147, 151

Yule, George, 22