By Fayez Gebali (auth.)
This textbook offers the mathematical thought and strategies important for studying and modeling high-performance worldwide networks, similar to the web. the 3 major development blocks of high-performance networks are hyperlinks, switching apparatus connecting the hyperlinks jointly and software program hired on the finish nodes and intermediate switches. This ebook offers the fundamental ideas for modeling and examining those final parts. issues lined contain, yet are usually not constrained to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.
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95. Find the joint pmf of X and Y . 1; 1/ D 0:1 0:95 D 0:095 Note that the sum of all the probabilities must add up to 1. 30 Individual pmf from a Given Joint pmf Sometimes we want to study an individual random variable even though our random experiment generates multiple RVs. 23. Assume a random experiment that generates two random variables X and Y with the given joint pmf. 32 Correlation 35 Find the individual pmf for X and Y . Are X and Y independent RVs? 31 Expected Value The joint pmf helps us find the expected value of one of the random variables.
We discuss two techniques in the following two subsections. 78) The above approximation is known as the DeMoivre–Laplace Theorem and is satisfactory even for moderate values of n such as when n 5. , Na 1), then DeMoivre–Laplace approximation is no longer valid. 80) Thus we are able to replace the binomial distribution with the Poisson distribution which is discussed in Sect. 27. 20. A file is being downloaded from a remote site and 500 packets are required to transmit the entire file. It has been estimated that on the average 5 % of received packets through the channel are in error.
In that case the variable t will indicate time. might also refer to the average number of bits in error for every 1,000 bits, say. In that case, the variable t would indicate the number of bits under consideration. In these situations we express the parameter a in the form a D t where expresses the rate of some event and t expresses the size or the period under consideration. 30 1 Probability Typically the Poisson distribution is concerned with the probability that a specified number of occurrences of event A take place in a specified interval t .
Analysis of Computer Networks by Fayez Gebali (auth.)