By George Kesidis

ISBN-10: 0470168684

ISBN-13: 9780470168684

This booklet is a quantitative textual content, which makes a speciality of the true concerns at the back of severe modeling and research of communications networks. the writer covers the entire priceless arithmetic and concept to ensure that scholars to appreciate the instruments that optimize machine networks this day.

- Covers either classical (e.g. queueing conception) and glossy (e.g. pricing) points of networking
- Integrates fabric on verbal exchange networks with fabric on modeling/analyzing and designing such networks
- Includes an answer Manual

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33) except that the 2;r term is replaced by the more general term (27r)"I2. REVIEW OF ELEMENTARY PROBABILITY THEORY for x E JR (a) Verify that E ( X l { X > 0)) = cc and that E ( - X l { X < 0)) = rn (b) Conclude that EX does not exist. Note that the question of existence is different from the question offiniteness. , for the LLSE estimator, the constants a and b are chosen so as to minimize the MSE. Show that the LLSE estimator is the conditional expectation E ( X / Y ) when the random variables X and Y are jointly Gaussian with var(Y) > 0 (so, in this case, the best estimator is a linear one).

I In other words. S,/n -+ p almost surely. So, S,/n is said to be a strongly consistent estimator of p. A proof of the strong LLN, which implies the weak LLN, is given in [44, 621. 12 FIRST-ORDER AUTOREGRESSIVE ESTIMATORS Given a series of samples X, at "times" n E {0,1! ), one may wish to iteratively estimate their mean. To this end, we can define X , as the "current" estimate of the mean. A typical problem in this context is that the underlying distribution of the samples is slowly changing with time.

1) This is called an n-dimensional distribution of X . The family of all such joint PMFs is called the set of jinite-dimensiond distributions (FDDs) of X . Note that the FDDs are consistent in that one can marginalize (reduce the dimension) and obtain another. , Beginning with a family of consistent FDDs, Kolmogorov's extension (or "consistency") theorem [104] is a general result demonstrating the existence of a stochastic process t + X , ( t ) ,u, E R, that possesses them. In the following sections, we will begin with a sample path definition of a Markov process and, from that, show how to derive its FDDs.

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