## Random signal analysis in engineering systems |

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### Contents

Random Variables and Vectors | 42 |

Functions of Random Variables | 89 |

Statistical Averages | 126 |

Copyright | |

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### Common terms and phrases

autocorrelation function axiom Bernoulli random variables binomial random variable characteristic function Chernoff bound components conditional density function conditional probability Consider continuous random variable Cov(X Cramer-Rao bound Determine the probability discrete random variables equal Example expected value fx(x FXY(x FXY(x,y fY(y fz(z Gaussian density function Gaussian distribution Gaussian random process Gaussian random variable Gaussian random vector independent random variables input integral interval joint density function likelihood function marginal density functions maximum likelihood estimator mean square value mutually independent random noise number of samples obtained oo<x<oo output P(comm parameter power spectral density probability assignment probability density function probability function probability of error Q function random numbers random process resistor Rx(t sample functions sample of mutually sample space shown in Fig signal simulation statistically independent statistically independent random Sx(f theoretical histogram tosses unbiased uncorrelated uniform random variables uniformly distributed Var(X wide sense stationary yields