Probability, Random Variables, and Random Processes

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Presentation transcript:

Probability, Random Variables, and Random Processes Chapter 04 Probability, Random Variables, and Random Processes

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.1 Relationship among sample space, events, and probability. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.2 Link configuration between points A and C. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.3 A partition of sample space S into n disjoint sets. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.4 Transition probability diagram of binary symmetric channel. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.5 (a) Link configuration between points A and D, (b) link configuration with permanently-failed link #5, and (c) link configuration with never-failing link #5. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.6 Relationship among sample space, random variable, and probability. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.7 (a) Continuous cdf and (b) discrete cdf. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.8 (a) pdf of a continuous random variable, (b) cdf of a continuous variable, (c) pdf of a discrete random variable, and (d) cdf of a discrete random variable. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.9 pdf of a Gaussian random variable with mean m and variance σ2. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.10 Area interpretation of Q(x) for Gaussian pdf. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.11 Rayleigh pdf with mean and variance . Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.12 pdfs for Example 4.13. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.13 Joint pdf and marginal pdfs for Example 4.18. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.14 (a) pdf of one variable, (b) pdf of sum of two variables, (c) pdf of sum of three variables, and (d) pdf of sum of four variables. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.15 (a) Slowly-fluctuating random processes; (b) rapidly-fluctuating random processes; and (c) autocorrelation functions of slowly and rapidly fluctuating processes. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.16 Power spectral density and autocorrelation function of white noise. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.17 (a) Extraction of in-phase and quadrature components and (b) generation of narrowband bandpass process. Copyright © 2016 Elsevier Inc. All rights reserved.

Copyright © 2016 Elsevier Inc. All rights reserved. Figure 4.18 (a) Power spectral density of bandpass white noise and (b) power spectral density of in-phase and quadrature components. Copyright © 2016 Elsevier Inc. All rights reserved.