Consider the following model to grow simple networks. At time t = 1 we start with acomplete network with no = 6 nodes. At each time step t> 1 a new node is added tothe network. The node arrives together with m = 2 new links, which are connected tom = 2 different nodes already present in the network. The probability II, that a newlink is connected to node i is:N(t-1)II₁=ki - 1Z==with Z = (k; -1)j=1where k; is the degree of node i, and N(t - 1) is the number of nodes in the network attimet - 1.(e) Write down the master equation of the model, i.e. the equation that describes theevolution of the average number N(t) of nodes that at time t have degree k.

Solution To write down the master equation for the evolution of the average number Nx(t) of nodes…

Answered: Consider the following model to grow…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For a parallel structure of identical components, the system can succeed if at least one of the components succeeds, Assume that components fail independently of each other and that each component has a 0.08 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It V be unusual to observe one component fail, since the probability that one component fails,, is V than 0.05. It V be unusual to observe two components fail, since the probability that two components fail,. is v than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) P Type here to search lyp
why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.25 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It be unusual to observe one component fail, since the probability that one component fails, is than 0.05. It be unusual to observe two components fail, since the probability that two components fail, is than 0.05. (Type integers or decimals. Do not round.)
Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.
Let us consider the population of people living in a city and its suburb and the migration within this population from the city and the suburbs to the city and the suburbs. The migration of these populations from and to each other is given by a stochastic matrix [.95 .03] P = |.05 .97 The entries in this matrix were obtained from collected data that demonstrates individuals are 95 % likely to remain in the city, 5 % likely to move from the city to the suburbs, 3 % likely to move from the suburbs to the city, and 97 % likely to remain in the suburbs. Now suppose in the year 2000 60 % or .6 percent of people live in the city and 40 % or .4 percent of people live in the suburbs. What will be the percentage of people living in the city be in the year 2001? What will be the percentage of people living in the suburbs be in 2002? Hint: Recall, for a general Markov Chain (S, ro, P) the initial vector ro is required to merely be a probability vector, that is, a vector whose entries add up to 1.…
V:55) Suppose G1 = ER1(3,0.5) and G2 = ER2(3,0.5) are two ER random graphs. What is the probability that they are isomorphic graphs?
3. suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.1 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day. [Hint: Note that (0, 0) is not a possible state.] (a) Construct the (one-step) transition matrix for this Markov chain. (b) Find the expected recurrence time for the state (1, 0).
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C021 (page 7 of 30) - Google Chrome Lom/mod/quiz/attempt.php?attempt3D1766745&cmid%3D875122&page%3D6 ING SYSTEM (ACADEMIC) ss Statistics 1 || Spring21 Time left 1:18: Suppose all 8 possible outcomes of an experiment are equally likely and denoted as E, E2, E3, E4, E5, E6, E7, and Eg. If A = {E,, E4, E5), then find P(A). a. 0.375 O b. 0.625
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The contingency table shows a random sample of urban, suburban, and rural libraries and the speed of their Internet access. In the table, mbps represents megabits per second. At α = 0.01 can you conclude that the metropolitan status of libraries and Internet access speed are related? Metropolitan status Access speed Urban Suburban Rural 1.4 mbps or less 5 20 58 1.5 mbps – 3.0 mbps 24 46 65 Greater than 3.0 mbps 37 59 64 What is the Chi-square test statistics and the decision for this question. The Test statistics is . Leave your answer in 3 decimal places. DECISION: We the null hypothesis.

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