Consider the following model to grow simple networks. At time t = 1 the network isformed by no = 3 nodes and mo= 1 link. At each time step t> 1 a new node is addedto the network. The node arrives together with 3 new links, which are connected to 3different nodes already present in the network. The probability II, that a new link isconnected to node j is:II;=kZwhere k; indicates the degree of node j, a € [0,1] and Z = 1k. Assume that fort>1 we can approximate Z as ZCt where C is a time-independent constant.(a) What is the total number of links in the network at time t? What is the totalnumber of nodes?(b) What is the average degree (k) of the network at time t? What is the averagedegree in the limit t∞?

Answered: Image /qna-images/answer/7e910864-d43b-4ce2-b59b-699422cf71aa.jpg

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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Given the situation where the failure of a structure is given according to the following condition: DeadLoad + LiveLoad is greater than the Resistance If the variables are acting independently from each other, and each one is normally distributed as follows: DeadLoad ~ N(100,25), LiveLoad ~ N(150,50) and Resistance ~ N(300,20). Compute the failure probability of the structure.
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 0.09 probability of failure. Complete parts (a) through (c) below. T.... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, 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.) (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.) O Time Remaining: 02:29:14 Next Left Raht
Moore’s portable X-ray equipment repair service shop receives an average of 6 portable X-ray sets per 8-hour day to be repaired. Moore would like to be able to tell his customers that they can expect one day service. What average repair time per set will the repair shop have to achieve to provide 1-day service on average? Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.
For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?
Define β1 stands for?
116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that…
Part II: Sections 2.1 - 2.7 8. Assume that X is a geometric random variable with p=0.32. (a) Compute P(X > 13[X > 3). (b) Compute E(X²).
Suppose Aaron recently purchased an electric car. The person who sold him his new car told him that he could consistently travel 200 mi before having to recharge the car's battery. Aaron began to believe that the car did not travel as far as the company claimed, and he decided to test this hypothesis formally. Aaron drove his car only to work and he recorded the number of miles that his new car traveled before he had to recharge its battery a total of 21 separate times. The table shows the summary of his results. Assume his investigation satisfies all conditions for a one-sample t-test. Mean miles traveled Sample size t-statistic P-value п P 185 21 -0.65 0.262 The results statistically significant at a = 0.05 because P 0.05. are are not >
A rat is put into the following maze: moves. 3 flat 1 The rat has a probability of 1/4 of starting in any compartment and suppose that the rat chooses a passageway at random when it makes a move from one compartment to another at each time. Let Xn be the compartment occupied by the rat after n 2 (d) Find the probability that the rat is in compartment 3 after two moves. (e) In the long run, how many times that the rat enters in compartment 4 in 100 movements?
Show that the average time till the first head is observed is y₁= p-¹, where p is the probability of getting a head each time the coin is tossed. Then find a closed form explicit solution to yn, the average time till n consecutive heads are observed for the first time.
the second photo is an example of resolution

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