By William L. Root Jr.; Wilbur B. Davenport
This "bible" of an entire iteration of communications engineers was once initially released in 1958. the point of interest is at the statistical concept underlying the learn of indications and noises in communications platforms, emphasizing concepts to boot s effects. finish of bankruptcy difficulties are provided.Sponsored by:IEEE Communications Society
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Additional info for An Introduction to the Theory of Random Signals and Noise
Discrete part and a continuous part. Probability Density Functions. Any continuous distribution function can be approximated as closely as we like by a nondecreasing staircase function, which can then be regarded as the probability distribution function of a discrete random variable. Thus a continuous random variable can always be approximated by a discrete one. However, a more direct method of analysis is made possible when the probability distribution function is not only continuous but also differentiable with a continuous derivative everywhere except possibly at a discrete set of points.
Similarly, by repeating the process, we can estimate the probability that k(n) dots will appear on the nth throw and also the joint probability that k(l) dots will appear on the first throw, that k(2) dots will appear on the second throw, . . , and that keN) dots will appear on the Nth throw, The specification of such a set of experiments with the corresponding probability functions and random variables (for all N) is said to define a random (stochastic) process and, in particular, a discrete-parameter random process.
Thus the discrete random variables z and yare statistically independent if and only if Eq. (3-38) is satisfied for all values of X and Y. Although Eq. (3-37) applies only to discrete random variables, Eq. (3-38) may be satisfied whether the random variables x and yare discrete, continuous, or mixed. We will therefore base our general definition of statistically independent random variables on Eq. (3-38). Thus: DEFINITION. • , and z are said to be statistically independent random variables if and only if the equation P(x s X,y ~ Y, .