By William L. Root Jr.; Wilbur B. Davenport

ISBN-10: 0470544147

ISBN-13: 9780470544143

ISBN-10: 0879422351

ISBN-13: 9780879422356

This "bible" of a complete new release of communications engineers used to be initially released in 1958. the point of interest is at the statistical thought underlying the learn of signs and noises in communications platforms, emphasizing options in addition s effects. finish of bankruptcy difficulties are provided.Sponsored by:IEEE Communications Society

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**Extra info for An Introduction to the Theory of Random Signals and Noise**

**Sample text**

ZN) have the following properties. First of all, (3-55) for all values of N, since all probability densities must be nonnegative. Further, we must have the relation J _ +IO • ••• J+IO P(Xl,X2, _ 10 . · · ,XN) dXl · • • tkN = 1 (3-56) corresponding to the fact that the probability that any possible event occurs is unity. Also, we must have the relation, following from Eq. (3-29), f +-II · ·· f +" -II P(Zl, • • • ,Xi,Xk+l, • • • ,XN)dXk+ 1 • • • = P(Xl, • • • ,Xi) tkN k

Let x and 11 be statistically independent random variables with the uniform probability density functions for 0 szsA for 0 and s vs B otherwise otherwise Determine and plot for A == 1 and B == 2 the probability density function of their product. 16. Let x and y be statistically independent random variables with the probability density functions () exp( -x '/2) p x == (2r)~ and p(1/) -I ~ exp (-t) for v~0 for'Y <0 Show that their product has an exponential probability density function (as in Probe 1).

10. Let x be the gaussian random variable of Probe 9. The random variable 1/ is defined by the equation xl/" when x ~ 0 11 == { -( -x) 1/" when x < 0 where n is a positive constant. Determine and plot the probability density function of the random variable 11 for the cases n - 1, 2, and infinity. 11. The random process x (t) is defined by x(t) - sin (wI + B) where tD is constant and where B is a random variable having the probability density function p(I) = \2 0: 0 for S B S 2lr otherwise a. Determine the probability distribution function Ptz, b.

### An Introduction to the Theory of Random Signals and Noise by William L. Root Jr.; Wilbur B. Davenport

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