Solution Manual for Probability Statistics and Random Processes for Engineers 4th Edition by Henry Stark - download pdf

Solution Manual for Probability Statistics and Random Processes for Engineers 4th Edition by Henry Stark\nSolution Manual for Probability Statistics and Random Processes for Engineers 4th Edition by Henry Stark\nFor courses in Probability and Random Processes.\nProbability, Statistics, and Random Processes for Engineers, 4e is a comprehensive treatment of probability and random processes that, more than any other available source, combines rigor with accessibility. Beginning with the fundamentals of probability theory and requiring only college-level calculus, the book develops all the tools needed to understand more advanced topics such as random sequences, continuous-time random processes, and statistical signal processing. The book progresses at a leisurely pace, never assuming more knowledge than contained in the material already covered. Rigor is established by developing all results from the basic axioms and carefully defining and discussing such advanced notions as stochastic convergence, stochastic integrals, and resolution of stochastic processes.\nTable of Contents\nPreface\n1 Introduction to Probability 1\n1.1 Introduction: Why Study Probability? 1\n1.2 The Different Kinds of Probability 2\nProbability as Intuition 2\nProbability as the Ratio of Favorable to Total Outcomes (Classical Theory) 3\nProbability as a Measure of Frequency of Occurrence 4\nProbability Based on an Axiomatic Theory 5\n1.3 Misuses, Miscalculations, and Paradoxes in Probability 7\n1.4 Sets, Fields, and Events 8\nExamples of Sample Spaces 8\n1.5 Axiomatic Definition of Probability 15\n1.6 Joint, Conditional, and Total Probabilities; Independence 20\nCompound Experiments 23\n1.7 Bayes’ Theorem and Applications 35\n1.8 Combinatorics 38\nOccupancy Problems 42\nExtensions and Applications 46\n1.9 Bernoulli Trials-Binomial and Multinomial Probability Laws 48\nMultinomial Probability Law 54\n1.10 Asymptotic Behavior of the Binomial Law: The Poisson Law 57\n1.11 Normal Approximation to the Binomial Law 63\nSummary 65\nProblems 66\nReferences 77\n2 Random Variables 79\n2.1 Introduction 79\n2.2 Definition of a Random Variable 80\n2.3 Cumulative Distribution Function 83\nProperties of FX(x) 84\nComputation of FX(x) 85\n2.4 Probability Density Function (pdf) 88\nFour Other Common Density Functions 95\nMore Advanced Density Functions 97\n2.5 Continuous, Discrete, and Mixed Random Variables 100\nSome Common Discrete Random Variables 102\n2.6 Conditional and Joint Distributions and Densities 107\nProperties of Joint CDF FXY (x, y) 118\n2.7 Failure Rates 137\nSummary 141\nProblems 141\nReferences 149\nAdditional Reading 149\n3 Functions of Random Variables 151\n3.1 Introduction 151\nFunctions of a Random Variable (FRV): Several Views 154\n3.2 Solving Problems of the Type Y = g(X) 155\nGeneral Formula of Determining the pdf of Y = g(X) 166\n3.3 Solving Problems of the Type Z = g(X, Y ) 171\n3.4 Solving Problems of the Type V = g(X, Y ), W = h(X, Y ) 193\nFundamental Problem 193\nObtaining fVW Directly from fXY 196\n3.5 Additional Examples 200\nSummary 205\nProblems 206\nReferences 214\nAdditional Reading 214\n4 Expectation and Moments 215\n4.1 Expected Value of a Random Variable 215\nOn the Validity of Equation 4.1-8 218\n4.2 Conditional Expectations 232\nConditional Expectation as a Random Variable 239\n4.3 Moments of Random Variables 242\nJoint Moments 246\nProperties of Uncorrelated Random Variables 248\nJointly Gaussian Random Variables 251\n4.4 Chebyshev and Schwarz Inequalities 255\nMarkov Inequality 257\nThe Schwarz Inequality 258\n4.5 Moment-Generating Functions 261\n4.6 Chernoff Bound 264\n4.7 Characteristic Functions 266\nJoint Characteristic Functions 273\nThe Central Limit Theorem 276\n4.8 Additional Examples 281\nSummary 283\nProblems 284\nReferences 293\nAdditional Reading 294\n5 Random Vectors 295\n5.1 Joint Distribution and Densities 295\n5.2 Multiple Transformation of Random Variables 299\n5.3 Ordered Random Variables 302\nDistribution of area random variables 305\n5.4 Expectation Vectors and Covariance Matrices 311\n5.5 Properties of Covariance Matrices 314\nWhitening Transformation 318\n5.6 The Multidimensional Gaussian (Normal) Law 319\n5.7 Characteristic Functions of Random Vectors 328\nProperties of CF of Random Vectors 330\nThe Characteristic Function of the Gaussian (Normal) Law 331\nSummary 332\nProblems 333\nReferences 339\nAdditional Reading 339\n6 Statistics: Part 1 Parameter Estimation 340\n6.1 Introduction 340\nIndependent, Identically Distributed (i.i.d.) Observations 341\nEstimation of Probabilities 343\n6.2 Estimators 346\n6.3 Estimation of the Mean 348\nProperties of the Mean-Estimator Function (MEF) 349\nProcedure for Getting a d-confidence Interval on the Mean of a Normal\nRandom Variable When sX Is Known 352\nConfidence Interval for the Mean of a Normal Distribution When sX Is Not\nKnown 352\nProcedure for Getting a d-Confidence Interval Based on n Observations on\nthe Mean of a Normal Random Variable when sX Is Not Known 355\nInterpretation of the Confidence Interval 355\n6.4 Estimation of the Variance and Covariance 355\nConfidence Interval for the Variance of a Normal Random\nvariable 357\nEstimating the Standard Deviation Directly 359\nEstimating the covariance 360\n6.5 Simultaneous Estimation of Mean and Variance 361\n6.6 Estimation of Non-Gaussian Parameters from Large Samples 363\n6.7 Maximum Likelihood Estimators 365\n6.8 Ordering, more on Percentiles, Parametric Versus Nonparametric Statistics 369\nThe Median of a Population Versus Its Mean 371\nParametric versus Nonparametric Statistics 372\nConfidence Interval on the Percentile 373\nConfidence Interval for the Median When n Is Large 375\n6.9 Estimation of Vector Means and Covariance Matrices 376\nEstimation of µ 377\nEstimation of the covariance K 378\n6.10 Linear Estimation of Vector Parameters 380\nSummary 384\nProblems 384\nReferences 388\nAdditional Reading 389\n7 Statistics: Part 2 Hypothesis Testing 390\n7.1 Bayesian Decision Theory 391\n7.2 Likelihood Ratio Test 396\n7.3 Composite Hypotheses 402\nGeneralized Likelihood Ratio Test (GLRT) 403\nHow Do We Test for the Equality of Means of Two Populations? 408\nTesting for the Equality of Variances for Normal Populations:\nThe F-test 412\nTesting Whether the Variance of a Normal Population Has a\nPredetermined Value: 416\n7.4 Goodness of Fit 417\n7.5 Ordering, Percentiles, and Rank 423\nHow Ordering is Useful in Estimating Percentiles and the Median 425\nConfidence Interval for the Median When n Is Large 428\nDistribution-free Hypothesis Testing: Testing If Two Population are the\nSame Using Runs 429\nRanking Test for Sameness of Two Populations 432\nSummary 433\nProblems 433\nReferences 439\n8 Random Sequences 441\n8.1 Basic Concepts 442\nInfinite-length Bernoulli Trials 447\nContinuity of Probability Measure 452\nStatistical Specification of a Random Sequence 454\n8.2 Basic Principles of Discrete-Time Linear Systems 471\n8.3 Random Sequences and Linear Systems 477\n8.4 WSS Random Sequences 486\nPower Spectral Density 489\nInterpretation of the psd 490\nSynthesis of Random Sequences and Discrete-Time Simulation 493\nDecimation 496\nInterpolation 497\n8.5 Markov Random Sequences 500\nARMA Models 503\nMarkov Chains 504\n8.6 Vector Random Sequences and State Equations 511\n8.7 Convergence of Random Sequences 513\n8.8 Laws of Large Numbers 521\nSummary 526\nProblems 526\nReferences 541\n9 Random Processes 543\n9.1 Basic Definitions 544\n9.2 Some Important Random Processes 548\nAsynchronous Binary Signaling 548\nPoisson Counting Process 550\nAlternative Derivation of Poisson Process 555\nRandom Telegraph Signal 557\nDigital Modulation Using Phase-Shift Keying 558\nWiener Process or Brownian Motion 560\nMarkov Random Processes 563\nBirth-Death Markov Chains 567\nChapman-Kolmogorov Equations 571\nRandom Process Generated from Random Sequences 572\n9.3 Continuous-Time Linear Systems with Random Inputs 572\nWhite Noise 577\n9.4 Some Useful Classifications of Random Processes 578\nStationarity 579\n9.5 Wide-Sense Stationary Processes and LSI Systems 581\nWide-Sense Stationary Case 582\nPower Spectral Density 584\nAn Interpretation of the psd 586\nMore on White Noise 590\nStationary Processes and Differential Equations 596\n9.6 Periodic and Cyclostationary Processes 600\n9.7 Vector Processes and State Equations 606\nState Equations 608\nSummary 611\nProblems 611\nReferences 633\nChapters 10 and 11 are available as Web chapters on the companion\nWeb site at http://www.pearsonhighered.com/stark.\n10 Advanced Topics in Random Processes 635\n10.1 Mean-Square (m.s.) Calculus 635\nStochastic Continuity and Derivatives [10-1] 635\nFurther Results on m.s. Convergence [10-1] 645\n10.2 Mean-Square Stochastic Integrals 650\n10.3 Mean-Square Stochastic Differential Equations 653\n10.4 Ergodicity [10-3] 658\n10.5 Karhunen-Lo`eve Expansion [10-5] 665\n10.6 Representation of Bandlimited and Periodic Processes 671\nBandlimited Processes 671\nBandpass Random Processes 674\nWSS Periodic Processes 677\nFourier Series for WSS Processes 680\nSummary 682\nAppendix: Integral Equations 682\nExistence Theorem 683\nProblems 686\nReferences 699\n11 Applications to Statistical Signal Processing 700\n11.1 Estimation of Random Variables and Vectors 700\nMore on the Conditional Mean 706\nOrthogonality and Linear Estimation 708\nSome Properties of the Operator ˆE 716\n11.2 Innovation Sequences and Kalman Filtering 718\nPredicting Gaussian Random Sequences 722\nKalman Predictor and Filter 724\nError-Covariance Equations 729\n11.3 Wiener Filters for Random Sequences 733\nUnrealizable Case (Smoothing) 734\nCausal Wiener Filter 736\n11.4 Expectation-Maximization Algorithm 738\nLog-likelihood for the Linear Transformation 740\nSummary of the E-M algorithm 742\nE-M Algorithm for Exponential Probability\nFunctions 743\nApplication to Emission Tomography 744\nLog-likelihood Function of Complete Data 746\nE-step 747\nM-step 748\n11.5 Hidden Markov Models (HMM) 749\nSpecification of an HMM 751\nApplication to Speech Processing 753\nEfficient Computation of P[E|M] with a Recursive\nAlgorithm 754\nViterbi Algorithm and the Most Likely State Sequence\nfor the Observations 756\n11.6 Spectral Estimation 759\nThe Periodogram 760\nBartlett’s Procedure—Averaging Periodograms 762\nParametric Spectral Estimate 767\nMaximum Entropy Spectral Density 769\n11.7 Simulated Annealing 772\nGibbs Sampler 773\nNoncausal Gauss-Markov Models 774\nCompound Markov Models 778\nGibbs Line Sequence 779\nSummary 783\nProblems 783\nReferences 788\nAppendix A Review of Relevant Mathematics A-1\nA.1 Basic Mathematics A-1\nSequences A-1\nConvergence A-2\nSummations A-3\nZ-Transform A-3\nA.2 Continuous Mathematics A-4\nDefinite and Indefinite Integrals A-5\nDifferentiation of Integrals A-6\nIntegration by Parts A-7\nCompleting the Square A-7\nDouble Integration A-8\nFunctions A-8\nA.3 Residue Method for Inverse Fourier Transformation A-10\nFact A-11\nInverse Fourier Transform for psd of Random Sequence A-13\nA.4 Mathematical Induction A-17\nReferences A-17\nAppendix B Gamma and Delta Functions B-1\nB.1 Gamma Function B-1\nB.2 Incomplete Gamma Function B-2\nB.3 Dirac Delta Function B-2\nReferences B-5\nAppendix C Functional Transformations and Jacobians C-1\nC.1 Introduction C-1\nC.2 Jacobians for n = 2 C-2\nC.3 Jacobian for General n C-4\nAppendix D Measure and Probability D-1\nD.1 Introduction and Basic Ideas D-1\nMeasurable Mappings and Functions D-3\nD.2 Application of Measure Theory to Probability D-3\nDistribution Measure D-4\nAppendix E Sampled Analog Waveforms and Discrete-time Signals E-1\nAppendix F Independence of Sample Mean and Variance for Normal\nRandom Variables F-1\nAppendix G Tables of Cumulative Distribution Functions: the Normal,\nStudent t, Chi-square, and F G-1\nIndex I-1\nFree Sample Solution Manual for Probability Statistics and Random Processes for Engineers 4th Edition by Henry Stark\nFor customer’s satisfaction, we provide free samples for any required Textbook solution or test bank to check and evaluate before making the final purchase..\nIf you require any further information, let me know. using Live Chat or Contact Us\nSolution Manual for Probability Statistics and Random Processes for Engineers 4th Edition by Henry Stark