Elements of Finite Probability

Preface......Page 5
Contents......Page 7
1.1 RANDOM EXPERIMENTS......Page 9
1.2 EMPIRICAL BASIS OF PROBABILITY......Page 11
1.3 SIMPLE EVENTS AND THEIR PROBABILITIES......Page 17
1.4 DEFINITION OF PROBABILITY MODEL......Page 22
1.5 UNIFORM PROBABILITY MODELS......Page 27
1.6 THE ALGEBRA OF EVENTS......Page 31
1.7 SOME LAWS OF PROBABILITY......Page 37
2.1 A MODEL FOR SAMPLING......Page 41
2.2 THE NUMBER OF SAMPLES......Page 47
2.3 ORDERED SAMPLING......Page 52
2.4 SOME FORMULAS FOR SAMPLING......Page 57
3.1 PRODUCT MODELS FOR TWO-PART EXPERIMENTS......Page 61
3.2 REALISM OF PRODUCT MODELS......Page 66
3.3 BINOMIAL TRIALS......Page 74
3.4 THE USE OF RANDOM NUMBERS TO DRAW SAMPLES......Page 79
4.1 THE CONCEPT OF CONDITIONAL PROBABILITY......Page 83
4.2 INDEPENDENCE......Page 89
4.3 TWO-STAGE EXPERIMENTS......Page 96
4.4 PROPERTIES OF TWO-STAGE MODELS; BAYES' LAW......Page 103
4.5 APPLICATIONS OF PROBABILITY TO GENETICS......Page 108
4.6 MARRIAGE OF RELATIVES......Page 115
4.7 PERSONAL PROBABILITY......Page 118
5.1 DEFINITIONS......Page 124
5.2 DISTRIBUTION OF A RANDOM VARIABLE......Page 128
5.3 EXPECTATION......Page 132
5.4 PROPERTIES OF EXPECTATION......Page 136
5.5 LAWS OF EXPECTATION......Page 140
5.6 VARIANCE......Page 146
6.1 THE BINOMIAL DISTRIBUTION......Page 154
6.2 THE HYPERGEOMETRIC DISTRIBUTION......Page 160
6.3 STANDARD UNITS......Page 166
6.4 THE NORMAL CURVE AND THE CENTRAL LIMIT THEOREM......Page 172
6.5 THE NORMAL APPROXIMATION......Page 176
6.6 THE POISSON APPROXIMATION FOR np = 1......Page 181
6.7 THE POISSON APPROXIMATION: GENERAL CASE......Page 184
6.8 THE UNIFORM AND MATCHING DISTRIBUTIONS......Page 189
6.9 THE LAW OF LARGE NUMBERS......Page 193
6.10 SEQUENTIAL STOPPING......Page 197
7.1 JOINT DISTRIBUTIONS......Page 202
7.2 COVARIANCE AND CORRELATION......Page 208
7.3 THE MULTINOMIAL DISTRIBUTION......Page 215
TABLES......Page 221
INDEX......Page 229
INDEX OF EXAMPLES......Page 235