By George Kesidis

ISBN-10: 0470168684

ISBN-13: 9780470168684

This publication is a quantitative textual content, which makes a speciality of the genuine matters in the back of severe modeling and research of communications networks. the writer covers the entire invaluable arithmetic and concept to ensure that scholars to appreciate the instruments that optimize computing device networks at the present time.

- Covers either classical (e.g. queueing idea) and smooth (e.g. pricing) features of networking
- Integrates fabric on communique networks with fabric on modeling/analyzing and designing such networks
- Includes an answer Manual

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**Example text**

When X and Y are both discretely distributed, we can similarly define their joint PMF p x , and ~ there is a similar condition for independence (the joint PMF is the product of the marginal PMFs). In general, a condition for independence is that the joint CDF is the product of the marginal CDFs. 4 at the end of the chapter. 1 Sums of independent random variables In this section we will consider sums of mutually independent continuous random variables. Our objective is to find the PDF of the sum given the PDF of the component random variables.

10 CONDITIONAL INDEPENDENCE the events A and C are said to be independent given B. , events A and C are (unconditionally) independent if P(A ( C ) = P(A). 19) implies P ( C I B, A) = P ( C I B). Conditional independence does not imply (unqualified) independence, as we will see in the following chapter. 11 A LAW OF LARGE NUMBERS In this section, we describe the basic connection between statistics and probability through the laws of large numbers (LLNs) [44,62,63]. Suppose we have an IID sequence of random A LAW OF LARGE NUMBERS 21 variables X I .

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). 14 For the gamma distribution. 8) and show that when r E Z+. 15 Use MGFs to prove that the binomial distribution with parameters n and q converges to the Poisson distribution with parameter X as q + 0 and n + x in such a way that nq + A.