Gregersen E. (editor) The Britannica Guide to Statistics and Probability
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7 The Britannica Guide to Statistics and Probability 7
330
König’s theorem, 214
Kuratowski, Kazimierz, 229
L
Lagrange, Joseph-Louis, 256,
280, 281
Landon, Alfred, 45
Laplace, Pierre-Simon de, 28,
31, 32, 33, 34, 38, 41, 256,
268–271, 280, 282, 295, 301
large numbers, law of, 64, 76–78,
80, 253, 302–303
large numbers, strong law of,
80, 84–85, 103
large numbers, weak law of,
80, 85
Latin square, 220–222
least squares approximation,
303–304, 310
least squares method, 139–141
least squares prediction, 92–94
Lebesgue, Henri-Léon, 88, 235
Lebesgue-measurable sets, class
of, 88
Lebesgue measure, 88, 90
Legendre, Adrien-Marie, 40,
271–274, 304
Leibniz, Gottfried Wilhelm, 28,
199, 251
Lévy, Paul, 99, 114
Lexis, Wilhelm, 44
Lucas, William F., 191
M
MacMahon, Percy Alexander, 200
MacNeish, H. F., 221
Manhattan Project, 288
Mann-Whitney-Wilcoxon test, 147
marginal distribution, 67, 68, 70
Markov, Andrey Andreyevich,
104, 305
Markov processes, 102, 104–105,
106, 107, 109, 305, 316, 318
martingale theory, 112–113
Maxwell, James Clerk, 39, 42,
255, 310
Maxwell-Boltzmann distribution
law, 42, 255, 298
McMullen, P., 238
measure theory, 84, 85–89
Mechain, Pierre, 272
Mendel, Gregor, 266, 294–295
Mersenne, Marin, 264
Mesner, D. M., 219
Mill, John Stuart, 33
minimal winning coalition
(MWC), 193, 194
minimax theorem, 165
Möbius, August Ferdinand,
211, 229
Möbius inversion theorem,
211–212
model building, 143–144
Moivre, Abraham de, 41, 78, 203,
274–275, 310
Morgenstern, Oskar, 74, 154, 165,
188, 189, 190, 191, 288
moves, theory of, 174–176
multinomial coefficients, 203
multinomial probability, 54–57
N
Nair, K. R., 219
Napoleonic Wars, 35
Nash, John F., 170, 275–276
331
7
Index 7
Nash equilibria, 179, 180, 183,
184, 187
Nash solution, 170–171
Natural Inheritance (Galton), 44
Neddermeyer, Seth, 288
Netto, Eugen, 200
Newton, Isaac, 99, 101, 233,
234, 245, 249, 264, 269,
274, 304
Neyman, Jerzy, 45, 47, 276–277
Nicole, Pierre, 26
Nightingale, Florence, 35
nonparametric methods,
146–148
nonprobability sampling
methods, 151
normal distribution 40, 42, 127,
308–310, 313
normal law, 42
Norwegian Central Bureau of
Statistics, 45
null hypothesis, 132
number theory, 201, 216,
233, 285
O
Observations on Man (Hartley), 31
Ornstein, Leonard Salomon, 101
Ornstein-Uhlenbeck process,
101, 104–105
orthogonal arrays, 222
Otter, Richard R., 226
outliers, 120–121
P
packing problem, 223
Parker, E. T., 221
partially balanced incomplete
block (PBIB) designs,
218–220
partitions, 205–206
Pascal, Blaise, 21, 23, 24, 26, 27,
258, 263, 264, 274, 311
Pascal’s triangle, 199
Pearson, Egon, 47
Pearson, Karl, 44, 47, 277–279
Pensées (Pascal), 26–27
permutations, 202, 209, 310–313
Perrin, Jean, 95
Petty, William, 33, 267, 268,
279–280
Philosophical Essay on Probabilities
(Laplace), 38
Planck, Max, 39
Platonic solids, 241
Poincaré, Henri, 199
Poisson, Siméon-Denis, 33, 81,
280–282, 295, 314
Poisson distribution, 64, 80–82,
91, 126, 282, 314–315
Poisson process, 94–95, 98, 104,
109, 112, 314, 318
poker, 156, 157, 287
Polya, George, 211, 225
Polya’s theorem, 211, 225, 226
population mean, estimation of,
129–131
Price, Richard, 31
Prisoners’ Dilemma (PD),
171–174, 175, 176, 183
probability, definition of,
48, 122
probability density functions,
89–91
probability distribution, 66–68,
70, 123–125, 127, 164
7 The Britannica Guide to Statistics and Probability 7
332
probability theory, 24, 32, 41, 48,
86, 87, 92, 110, 112, 199, 254,
287, 317
applications of, 50–53, 58
independence in, 63–64
Q
Quetelet, Adolphe, 35–36, 37, 38,
39, 42, 282–283, 295–296
queuing models, 108–110
queuing theory, 315–316
R
Ramsey, Frank Plumpton, 74, 214
Ramsey’s numbers, 214–215
Ramsey’s theorem, 201, 214
randomization, 45
randomized block design,
136, 137
random sampling, 152
random variables, 65–66, 123,
124, 125
real-valued functions, 65
recurrence relations, 204
regression analysis, 138, 142, 144
regression model, 138–139, 142
regression to the mean, 43
relative frequency interpreta-
tion, 76–77
religion, 27, 32
Renaissance, 24
residual analysis, 142–143
Riemann, Bernhard, 282
Roosevelt, Franklin Delano, 45
Rota, Gian-Carlo, 212
Royal Society of London, 27, 31,
249, 268, 280, 286
S
saddlepoint, 160, 162
Salk vaccine, 51
sample statistics, 128–129
sample survey methods, 150–152
sampling, 316–318
sampling error, 151
Savage, Leonard J., 74
Schläfli, Ludwig, 238
Schrödinger, Erwin, 287
scientific revolution, 17th
century, 24
self-avoiding random walk,
212, 213
Shannon, Claude, 286
Shrikhande, S. S., 221
significance testing, 142
Smith, John Maynard, 176,
177, 178
social physics, 36, 38
social statistics, 39
Spearman rank correlation
coefficient, 147–148
Sperner’s theory, 201
standard deviation, 120, 121, 125,
127, 308, 318
stationary processes, 102–103
statistical decision theory, 152
statistical inference, 127, 150
statistical mechanics, 201,
254, 255
statistical physics, 38–39
statistical process control, 148,
149–150
statistical quality control, 148
statistics
definition of, 115
descriptive, 116–117
333
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Index 7
Steiner, Jakob, 200, 237,
283–284
Stirling, James, 275
stochastic processes, 82, 94, 95,
99, 111, 318–319
definition of, 102
types of, 102–104
Stokes’s law, 99
St. Petersburg paradox, 28
Student’s t-test, 319–320
subjective probability, 73
Sudoku, 198
Süssmilch, Johann Peter, 34
Sylvester, James Joseph, 199, 209,
238, 242, 260, 284–286
Sylvester’s formula, 210
symbolic logic, 199
symmetric random walk,
107–108
Szekeres, George, 215
T
Tartaglia, Niccolò, 258
Theory of Games and Economic
Behavior, The (Morgenstern
and von Neumann), 154
thermodynamics, second law of,
39, 105, 106, 107
time series, 145
total probability, law of, 72
Tucker, Albert W., 171
Turing, Alan, 286
U
Uhlenbeck, George Eugene, 101
United Nations Security
Council, 195
U.S. Electoral College, 195
U.S. Public Health Service, 52
utility function, 73
utility theory, 165–166
V
variance, 70–72
Viète, François, 264
von Neumann, John, 74, 154,
165, 188, 189, 190, 191,
286–290
von Neumann–Morgenstern
theory, 188–191
voting, 183–188, 192,
193–194, 195
W
Wagner, K., 229
Wallis, John, 251
Weldon, Walter F. R., 44,
278, 279
Wiener, Norbert, 85, 98
Wiener process, 95
Wilcoxon signed-rank
test, 147
Wilson, R. M., 222
Wit, Jan de, 25
World War II, 46, 314
Y
Yates, Frank, 200
Yule, George Udny, 44, 279
Z
Zermelo, Ernst, 159
