Index

Acceptance sampling 32Addition Theorem 10, 25α 135Alternative hypothesis 134Analysis of variance 197Average outgoing quality 34Axioms of Probability 8

Bayes’ theorem 45β 137Binomial coefficients 24Binomial probability

distributuion 64, 244Mean 69Variance 69

Binomial theorem 3, 11, 15, 24, 83Birthday problem 8, 16Bivariate random

variables 115

Cancer test 42Central limit theorem 121, 123, 213Cereal Box Problem 88Chi squared distribution 141Choosing an assistant 30Combinations 22, 242Conditional probability 10, 39, 40Confidence coefficient 131, 149Confidence interval 131Confounding 233Control charts 155

Mean 159, 160np 161p 163

Correlation coefficient 200Counting principle 19Critical region 135

Degrees of freedom 143Derangements 17Difference equation 241Discrete uniform distriution 59Drivers’ed 39

e 5, 6, 26, 31Estimation 130, 177Estimating σ 157, 159Expectation 6

Binomial distribution 69Geometric distribution 73Hypergeometric distribution 71Negative Binomial distribution 88Negative Hypergeometric

distribution 102

F ratio distribution 148Factor 224Factorial experiment 231, 232Finite population correction

factor 71, 214Fractional factorial experiment 234

Ganbler’s ruin 248General addition theorem 10, 25Generating functions 252Geometric probability 48Geometric probability distribution 72, 84Geometric series 12, 13German tanks 28, 62, 177

Hat problem 5, 26Heads before tails 88Hypergeometric probability distribution

70, 105, 247Hypothesis testing 133

A Probability and Statistics Companion, John J. KinneyCopyright © 2009 by John Wiley & Sons, Inc.

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260 Index

Inclusion and exclusion 26Independent events 11Indianapolis 500 data 196Influential observations 193Interaction 225

Joint probability distributions 115

Least squares 191Let’s Make a Deal 8, 15, 17, 44Lower control limit 158Lunch problem 96

Marginal distributions 117Maximum 176Mean 60

Binomial distribution 69, 246Geometric distribution 73Hypergeometric distribution 71Negative Binomial distribution 88Negative Hypergeometric

distribution 174Mean of means 124Means - two samples 150Median 28, 174Median - median line 202, 207Meeting at the library 48Minimum 174, 177Multiple regression 235Multiplication rule 10Mutually exclusive events 9Mythical island 84

Negative binomial distribution 87, 103Negative hypergeometric distribution 99Nonlinear models 201Nonparametric methods 170Normal probability distribution 113Null hypothesis 134

Operating characteristic curve 138Optimal allocation 217Order statistics 173, 174

p-value for a test 139Patterns in binomial trials 90Permutations 5, 12, 19, 242

Some objects alike 20Poisson distribution 250Poker 27

Pooled variances 152Power of a test 137Probability 2, 8Probability distribution 32, 59Proportional allocation 215

Race cars 28, 64Random variable 58Randomized response 46, 55Range 156, 176Rank sum test 170Ratio of variances 148Recursion 91, 101, 241Residuals 189Runs 3, 180, 182

Theory 182Mean 184Variance 184

Sample space 2, 4, 6, 7, 10, 14Sampling 211Seven game series in sports 75Significance level 135Simple random sampling 211Standard deviation 60Strata 214, 221Student t distribution 146Sums 62, 69, 111, 121

Type I error 135Type II error 135

Unbiased estimator 212Uniform random variable 59, 109Upper control limit 158

Variance 60, 119Binomial distribution 69Hypergeometric distribution 71Negative Binomial distribution 88Negative Hypergeometric

distribution 102

Waiting at the library 48Waiting time problems 83World series 76

Yates algorithm 230