622 Index
Permutation, 63
Pie chart, 12
Point estimator, 240–241
evaluation, 266–272
mean square error, 266–271
unbiased estimator, 267
Poisson, S. D., 148
Poisson distribution function, 155–156
Poisson process, 179–181
Poisson random variable
applications, 150–153
definition, 148
moment generating function, 149–150, 154
square root, 389–390
tests concerning Poisson distribution mean,
330–333
Polynomial regression, 391–394
Pooled estimator, 259, 315
Population, 3, 201
Population mean, 202
Population variance, 202
Positively correlated, 36
Poskanzer, D., 329
Posterior density function, 273, 276
Power function, 298
Prediction interval, future response in regression,
373–375, 410
Prior distribution, 272, 275–277
Probability
axioms, 59–61
conditional, 67–70
frequency interpretation, 55
subjective interpretation, 55
Probability density function
joint probability density function, 99–100
random variable, 93–95
sample means, 203
Probability mass function
binomial random variable, 142
joint probability mass function, 96
marginal probability mass function, 98
random variable, 92
Probit model, 412
Pseudo random number, 251
p-value, 296, 303–304, 309, 311
Q
Quadratic regression equation, 393
Quality control,seeControl charts
Quartiles, 25–27R
Randomness, runs test, 533–536
Random number, 163
Random sample, 217
Random variable
Bernoulli random variable, 141
binomial random variable, 141–148
chi-square distribution, 185–187
conditional distributions, 105–107
continuous random variable, 91, 93
covariance
definition, 121–122
properties, 122–123
sums of random variables, 125–126
definition, 89–90
discrete random variable, 91–92
distribution function, 91–93
entropy, 109–111
expectation, 107–118
exponential random variables, 175–181
F-distribution, 191–192
gamma distribution, 182–185
hypergeometric random variable, 156–160
independent random variables, 101–105
indicator random variable, 90–91
jointly distributed random variables, 95–101
logistics distribution, 192–193
moment generating functions, 126–127
normal random variables, 168–175
Poisson random variable, 148–156
probability density function, 93–95
probability mass function, 92
sums of random variables, expected value,
115–118
t-distribution, 189–191
uniform random variable, 160–168
variance
definition, 118–120
standard deviation, 121, 126
sums of random variables, 123–125