Probability and Statistics with Reliability, Queuing and Computer Science Applications

Contents......Page 3
Acronyms......Page 12
Website......Page 15
Introduction......Page 16
PROBABILITY MODELS......Page 17
SAMPLE SPACE......Page 18
EVENTS......Page 21
ALGEBRA OF EVENTS......Page 22
GRAPHICAL METHODS OF REPRESENTING EVENTS......Page 26
PROBABILITY AXIOMS......Page 28
COMBINATORIAL PROBLEMS......Page 34
CONDITIONAL PROBABILITY......Page 39
INDEPENDENCE OF EVENTS......Page 41
BAYES’ RULE......Page 53
BERNOULLI TRIALS......Page 62
Discrete Random Variables......Page 79
RANDOM VARIABLES AND THEIR EVENT SPACES......Page 80
THE PROBABILITY MASS FUNCTION......Page 82
DISTRIBUTION FUNCTIONS......Page 84
SPECIAL DISCRETE DISTRIBUTIONS......Page 86
ANALYSIS OF PROGRAM MAX......Page 111
THE PROBABILITY GENERATING FUNCTION......Page 115
DISCRETE RANDOM VECTORS......Page 118
INDEPENDENT RANDOM VARIABLES......Page 124
Continuous Random Variables......Page 135
EXPONENTIAL DISTRIBUTION......Page 139
RELIABILITY & FAILURE RATE......Page 144
SOME IMPORTANT DISTRIBUTIONS Hypoexponential Distribution......Page 149
FUNCTIONS OF A RANDOM VARIABLE......Page 168
JOINTLY DISTRIBUTED RANDOM VARIABLES......Page 173
ORDER STATISTICS......Page 177
DISTRIBUTION OF SUMS......Page 188
FUNCTIONS OF NORMAL RANDOM VARIABLES......Page 204
Expectation......Page 215
EXPECTATION BASED ON MULTIPLE RANDOM VARIABLES......Page 223
TRANSFORM METHODS......Page 230
MOMENTS AND TRANSFORMS OF SOME DISTRIBUTIONS......Page 240
COMPUTATION OF MEAN TIME TO FAILURE......Page 252
INEQUALITIES & LIMIT THEOREMS......Page 261
Conditional Distribution & Expectation......Page 270
MIXTURE DISTRIBUTIONS......Page 279
CONDITIONAL EXPECTATION......Page 286
IMPERFECT FAULT COVERAGE AND RELIABILITY......Page 293
Stochastic Processes......Page 314
CLASSIFICATION OF STOCHASTIC PROCESSES......Page 320
THE BERNOULLI PROCESS......Page 326
THE POISSON PROCESS......Page 330
RENEWAL PROCESSES......Page 340
AVAILABILITY ANALYSIS......Page 345
RANDOM INCIDENCE......Page 355
RENEWAL MODEL OF PROGRAM BEHAVIOR......Page 359
Discrete-Time Markov Chains......Page 363
COMPUTATION OF n-STEP TRANSITION PROBABILITIES......Page 368
STATE CLASSIFICATION & LIMITING PROBABILITIES......Page 374
DISTRIBUTION OF TIMES btw STATE CHANGES......Page 383
MARKOV MODULATED BERNOULLI PROCESS......Page 385
IRREDUCIBLE FINITE CHAINS WITH APERIODIC STATES......Page 388
M/G/ 1 QUEUING SYSTEM......Page 403
DISCRETE-TIME BIRTH–DEATH PROCESSES......Page 412
FINITE MARKOV CHAINS WITH ABSORBING STATES......Page 419
Continuous-Time Markov Chains......Page 432
THE BIRTH–DEATH PROCESS......Page 439
OTHER SPECIAL CASES OF THE BIRTH–DEATH MODEL......Page 476
NON-BIRTH–DEATH PROCESSES......Page 485
MARKOV CHAINS WITH ABSORBING STATES......Page 530
SOLUTION TECHNIQUES......Page 552
AUTOMATED GENERATION......Page 563
Networks of Queues......Page 588
OPEN QUEUING NETWORKS......Page 593
CLOSED QUEUING NETWORKS......Page 601
GENERAL SERVICE DISTRIBUTION AND MULTIPLE JOB TYPES......Page 631
NON-PRODUCT-FORM NETWORKS......Page 639
COMPUTING RESPONSE TIME DISTRIBUTION......Page 652
SUMMARY......Page 665
Statistical Inference......Page 671
PARAMETER ESTIMATION......Page 673
HYPOTHESIS TESTING......Page 728
Regression & Analysis of Variance......Page 763
LEAST-SQUARES CURVE FITTING......Page 768
THE COEFFICIENTS OF DETERMINATION......Page 772
CONFIDENCE INTERVALS IN LINEAR REGRESSION......Page 775
TREND DETECTION AND SLOPE ESTIMATION......Page 778
CORRELATION ANALYSIS......Page 781
SIMPLE NONLINEAR REGRESSION......Page 784
HIGHER-DIMENSIONAL LEAST-SQUARES FIT......Page 785
ANALYSIS OF VARIANCE......Page 788
Biblio......Page 801
Properties of Distributions......Page 814
Statistical Tables......Page 817
Laplace Transforms......Page 838
Program Performance Analysis......Page 845
Index......Page 847