## Applied Probability and Stochastic Processes: In Engineering and Physical SciencesThis introduction to modern concepts of applied stochastic processes is written for a broad range of applications in diverse areas of engineering and the physical sciences (unlike other books, which are written primarily for communications or electrical engineering). Emphasis is on clarifying the basic principles supporting current prediction techniques. The first eight chapters present the probability theory relevant to analysis of stochastic processes. The following nine chapters discuss principles, advanced techniques (including the procedures of spectral analysis and the development of the probability density function) and applications. Also features material found in the recent literature such as higher-order spectral analysis, the joint probability distribution of amplitudes and periods and non-Gaussian random processes. Includes numerous illustrative examples. |

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### Contents

Random Variables and Their Probability Distributions | 13 |

Moments of Random Variables | 43 |

Moment Generating Function Characteristic Function | 72 |

Copyright | |

18 other sections not shown

### Common terms and phrases

amplitude assume autocorrelation function binomial distribution called Chapman-Kolmogorov equation characteristic function coefficient conditional probability confidence interval covariance crest-to-trough excursions cumulative distribution function Definition degrees of freedom denoted derived distribution given distribution with mean domain equal estimator evaluated event expected value Fourier transform frequency response function function is given gamma distribution Gaussian random process given in Eq Hence independent random variables input integration joint probability density let us consider linear system Markov process mean and variance mean value narrow-band nonlinear system normal distribution obtained output Poisson distribution Poisson process positive maxima Pr{X probability density function probability mass function random phenomena random process random process x(t Rayleigh distribution respectively sample space Section shown in Figure spectral density function stationary statistically independent stochastic process Sxx(u tion transition probability type random variable Var[x wave Wiener-Levy process written x2 distribution Xv X2 zero mean