Appendix B

Appendix B - Index 437 Independent increment processes, 343...

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Unformatted text preview: Index 437 Independent increment processes, 343 Independent random variables binomial, 214 description of, 182–183 Poisson, 214–215 sums of description of, 202–218 s-transform of the probability density function of the, 247–249 z-transform of the probability mass function of the, 255 two maximum of, 219–221 minimum of, 218–219 Inductive statistics, 395 Inequality Chebyshev, 102–103, 402 Markov, 103–104 Infinite impulse response system, 319–320 Interconnection models, 221–222 Intersection(s) associative law for, 11 commutative law for, 11 of events, 3–4 of sets, 9, 11 Interval estimate, 403 Irreducible Markov chain, 363 J Joint cumulative distribution function of bivariate random variables, 167–169 probabilities determined from, 175–177 Joint probability density function, 173 Joint probability mass function description of, 169, 177 for Poisson processes, 346 K k th-order Erlang random variable, 137, 154 L Lag time, 270 Laws of large numbers, 226–227 “Least-squares” line, 419 Left-tail test, 414 Level of significance, 412, 414 Likelihood function, 405 Limiting-state probabilities, 366–369 Linear correlation, 185 Linear functions, of one random variable description of, 198–199 moments of, 201–202 Linear regression, 418–421 Linear systems autoregressive moving average process, 316–323 with continuous-time random inputs, 307–313 with deterministic inputs, 305–307 with discrete-time random inputs, 313–315 M Maclaurin’s series expansion, 123 Marginal probability density function, 173 Marginal probability mass function, 169–170 Markov chains continuous-time birth processes, 373–376 death processes, 373–376 description of, 370–373 definition of, 358 discrete-time description of, 359 doubly stochastic matrix, 369–370 limiting-state probabilities, 366–369 n-step state transition probability, 360–361 states, 363–366 state transition diagrams, 361–363, 365 state transition probability, 359–360 gambler’s ruin as, 376–377 homogeneous, 359 irreducible, 363 nonhomogeneous, 359 time homogeneous, 371 Markov inequality, 103–104 Markov processes classification of, 359 description of, 358–359 Markov chains. See Markov chain Markov property, 358 Maximum likelihood estimation, 405–408 Mean arithmetic, 85 conditional, 180–181 of discrete-time random process, 290 of random process, 270 sample, 397–399 Mean squared error estimation, 408–411 Mean-square value, 278 Measure of central tendency, 85 Memoryless property of the exponential distribution, 134–136 of the geometric distribution, 121 438 Index Minimum mean squared error estimation, 408–411 Modified geometric distribution, 119–120 Moments of characteristic function, 243–244 of a linear function, 201–202 of random variables, 90–101 of s-transform, 245–246 of the sum of random variables, 209–210 of z-transform, 252–253 Moving average process definition of, 316 description of, 316–319 Multinomial distributions, 189–190...
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This note was uploaded on 01/05/2010 for the course STAT 350 taught by Professor Carlton during the Fall '07 term at Cal Poly.

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Appendix B - Index 437 Independent increment processes, 343...

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