A Primer in Probability, Second Edition

CRC Press, Jul 27, 1990 - Mathematics - 336 pages
Somewhat revised/expanded new edition of a problem-oriented introductory undergraduate text, the first edition of which appeared about a decade ago. The author writes with courteous clarity, and imposes only modest demands upon the mathematical skills of her readers. Problems at the end of each of t

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Contents

 A First Glimpse of Probability 1 DETERMINISTIC OR RANDOM 3 14 INTERPRETING PROBABILITY 4 PROBLEMS 6 Basic Concepts of Probability 9 22 EVENTS AND THEIR PROBABILITIES 10 23 COMBINING EVENTS 12 24 PROBABILITIES ASSOCIATED WITH COMBINED EVENTS 14
 PROBLEMS 132 Describing the Joint Behavior of Several Random Variables 139 82 COVARIANCE 140 83 EXPECTATION OF THE SUM OF SEVERAL RANDOM VARIABLES 144 84 VARIANCE OF THE SUM OF SEVERAL RANDOM VARIABLES 145 85 CORRELATION COEFFICIENT 148 86 PROBLEMS CONCERNING SEVERAL RANDOM VARIABLES 150 87 RANDOM VARIABLES BASED ON SAMPLES 155

 25 FINDING PROBABILITIES 20 PROBLEMS 23 Counting Procedures and Their Applications in Computing Probabilities 31 32 COUNTING PROCEDURES INVOLVING ORDER RESTRICTIONS 33 33 COUNTING PROCEDURES NOT INVOLVING ORDER RESTRICTIONS 36 34 APPLICATIONS OF COUNTING PROCEDURES 37 ROLE OF DISTINGUISHABILITY 43 36 RANDOM SAMPLING 46 PROBLEMS 51 Conditional Probability 59 42 MULTIPLICATION RULE AND ASSIGNING PROBABILITIES 65 43 STAGEWISE EXPERIMENTS 67 BAYES RULE 70 PROBLEMS 74 Independence 81 52 INDEPENDENCE FOR MORE THAN TWO EVENTS 85 53 PROBABILITIES ASSOCIATED WITH MUTUALLY INDEPENDENT EVENTS 86 PROBLEMS 91 Random Variables 97 62 CUMULATIVE DISTRIBUTION FUNCTION 103 63 FUNCTIONS OF A RANDOM VARIABLE 106 64 JOINT PROBABILITY FUNCTIONS 107 65 MARGINAL PROBABILITY FUNCTIONS 109 66 INDEPENDENCE 110 PROBLEMS 113 Describing Random Variables and Their Distributions 121 72 LAWS OF EXPECTATION FOR A SINGLE RANDOM VARIABLE 125 73 VARIANCE 126 74 LAWS OF VARIANCE FOR A SINGLE RANDOM VARIABLE 130 75 STANDARDIZED RANDOM VARIABLES 131
 PROBLEMS 158 Special Discrete Probability Models 165 92 WAITING TIME DISTRIBUTIONS 171 93 POISSON DISTRIBUTION 176 94 HYPERGEOMETRIC DISTRIBUTION 180 95 SUMS OF BINOM1AL RANDOM VARIABLES 186 96 MULTINOMIAL DISTRIBUTION 191 PROBLEMS 194 Statistical Inference 201 102 TESTING FOR GOODNESS OF FIT 205 103 TESTS FOR COMPARING TWO GROUPS 209 PROBLEMS 211 Continuous Distributions 217 112 NORMAL DISTRIBUTION 219 PROBLEMS 225 Limit Theorems 229 122 LAW OF LARGE NUMBERS 232 123 CENTRAL LIMIT THEOREM 233 124 APPROXIMATING DISCRETE DISTRIBUTIONS USING THE CENTRAL LIMIT THEOREM 234 PROBLEMS 245 Summation and Subscripts 249 Set Theory 253 Mathematical Induction as a Method of Proof 257 Binomial Expansions 261 Infinite Series 267 Tables 271 Answers to Selected Problems 285 Index 315 Copyright