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ProbabilityStatisticsRandomProc

# ProbabilityStatisticsRandomProc - PROBABILITY STATISTICS...

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Tom Penick www.teicontrols.com/notes ProbabilityStatisticsRandomProc.pdf 5/18/2001 Page 1 of 25 PROBABILITY, STATISTICS, AND RANDOM PROCESSES EE 351K INDEX ! factorial . ................... 3, 24 1 st fundamental theorem of probability. ..................... 16 2 nd fundamental theorem of probability. ..................... 17 absorbing matrices. ........... 21 absorption probability. .................. 21 time . ........................... 21 approximation theorem. ....18 area sphere. ........................ 25 Bayes' formula . ................ 11 Bayes' inverse problem. ....11 Bayes' theorem. ................ 11 Bernoulli trials central limit theorem. ...17 Bernoulli trials process. ..6, 7 beta density function. ........ 12 binomial coefficient. ........... 5 binomial distribution central limit theorem. negative . ....................... 7 binomial distribution function ........................................ 6 binomial expansion. .......... 25 binomial theorem . ............ 25 birthday problem. ............. 23 B-matrix. .......................... 21 calculus. ........................... 24 canonical form . ................ 21 card problem. ................... 23 central limit theorem. ........ 17 general form. ............... 18 sum of discrete variables .............................. 18 central limit theorem for Bernoulli trials. ............... 17 central limit theorem for binomial distributions. ....17 Chebyshev inequality . ...... 16 coefficient binomial. ....................... 5 multinomial. .................. 5 coefficients of ordinary generating function. ........ 20 combinations. ..................... 3 conditional density function continuous. .................. 11 conditional probability 10, 11 continuous conditional density function. ............. 11 continuous uniform density.9 convolution. ..................... 15 example . ..................... 16 correlation. ....................... 15 covariance. ....................... 15 cumulative distribution function. ........................... 6 cumulative normal distribution function. ......... 6 cyclic permutation. ............. 3 D ( X ) standard deviation. ..14 De Morgan’s laws . ........... 10 density function. ................. 8 beta. ............................ 12 exponential. ................... 9 joint. ............................. 9 normal . ......................... 8 standard normal. ............ 8 dependent variable. ........... 25 derangement. .................... 25 derivatives. ....................... 24 deviation. ......................... 14 disoint. ............................... 3 distribution hypergeometric. ............. 7 uniform. ...................... 25 distribution function . 5, 6, 25 binomial. ....................... 6 cumlative . ..................... 6 discrete uniform . ........... 5 exponential. ................... 8 geometric. ..................... 7 joint. ............................. 7 joint cumulative. ............ 6 multinomial. .................. 7 negative binomial. ......... 7 poisson. ......................... 7 double coin toss. ................. 2 e natural number. ............. 24 E ( X ) expected value. ........ 12 envelope problem. ............ 23 ergodic chain. ................... 22 Euler's equation. ............... 24 events independent. .................. 4 e x infinite sum . ................ 24 expectation properties. ................... 13 expectation of a function. ..13 expectation of a product. ...13 expected value. ......... 6, 8, 12 exponential density function9 exponential distribution . ..... 8 f ( t ) exponential density function. ........................... 9 f ( x ) density function. .......... 8 F ( x,y ) joint cumulative distribution function. ......... 6 f ( x,y ) joint density function 9 f ( ϖ ) continuous uniform density function. ............... 9 factorial. ....................... 3, 24 failure rate. ......................... 9 fixed probability matrix. ...22 fixed probability vector. ....22 fundamental matrix. .... 21, 22 F X ( x ) cumulative normal distribution function. ......... 6 f X ( x ) normal density function ........................................ 8 g ( t ) generating function. ..18, 19 general math. .................... 24 generating function. .... 18, 19 ordinary . ..................... 19 properties. ................... 20 geometric distribution. ........ 7 glossary. ........................... 25 graphing terminology . ...... 25 h ( z ) ordinary generating function. ......................... 19 hat check problem. ........... 23 hypergeometric distribution 7 hypotheses . ...................... 11 inclusion-exclusion principle ........................................ 3 independent events . ............ 4 independent trials. ............ 25 independent variable. ........ 25 inequality Chebyshev . ................. 16 Markov . ...................... 13 infinite sample space . ......... 3 infinite sum. ..................... 24 integration. ....................... 24 intersection. ........................ 3 joint cumulative distribution function. ........................... 6 joint density function. ......... 9 joint distribution. ................ 7 L’Hôpitol’s rule. ............... 24 law of averages. ................ 16 law of large numbers. ....... 16 linearizing an equation. ..... 25 logarithms.

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ProbabilityStatisticsRandomProc - PROBABILITY STATISTICS...

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