## Probability, random variables, and random signal principlesToday, any well-designed electrical engineering curriculum must train engineers to account for noise and random signals in systems. The best approach is to emphasize fundamental principles since systems can vary greatly. Professor Peebles's book specifically has this emphasis, offering clear and concise coverage of the theories of probability, random variables, and random signals, including the response of linear networks to random waveforms. By careful organization, the book allows learning to flow naturally from the most elementary to the most advanced subjects. Time domain descriptions of the concepts are first introduced, followed by a thorough description of random signals using frequency domain. Practical applications are not forgotten, and the book includes discussions of practical noises (noise figures and noise temperatures) and an entire special chapter on applications of the theory. Another chapter is devoted to optimum networks when noise is present (matched filters and Wiener filters). This third edition differs from earlier editions mainly in making the book more useful for classroom use. Beside the addition of new topics (Poisson random processes, measurement of power spectra, and computer generation of random variables), the main change involves adding many new end-of-chapter exercises (180 were added for a total of over 800 exercises). The new exercises are all clearly identified for instructors who have used the previous edition. |

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### Contents

The Random Variable | 33 |

Operations on One Random | 60 |

Multiple Random Variables | 77 |

Copyright | |

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### Common terms and phrases

Advanced Book Program applied assumed autocorrelation function available power gain band-limited bandpass bandwidth called Chapter characteristic function co0t corresponds covariance cross-correlation function cross-power denoted discrete random variable effective input noise elements events defined Example expected value experiment Find and sketch Fourier transform frequency function fx(x fY(y gaussian random variable given H(co impulse response input noise temperature integral joint density function joint distribution function jointly wide-sense stationary linear system lowpass matched filter mean value mean-squared noise power noise temperature obtain permission of publishers power density spectrum power spectrum Problem properties publishers Addison-Wesley random process X(t random signal random variables Xt real constants real number real positive constants resistor Rxx(t RxY(t sample function sample space shown in Figure signal x(t SNN(co spot noise figure stationary process statistically independent subsets Sxx(co transfer function uncorrelated variance voltage waveform white noise X(co