Suppose that the random variable X has an exponential distribution with parameter ? > 0. (i) What

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Suppose that the random variable X has an exponential distribution with parameter ? > 0. (i) What are the probability density function, fX(x), and the probability distribution function, FX(x), for the random variable X? [2 marks] (ii) Derive the mean and variance of the random variable X and determine its coefficient of variation. [3 marks] (iii) Show that the random variable X obeys the memoryless property P(X > t + s|X > t) = P(X > s) for all s, t > 0. [2 marks] (iv) Use the inverse transform method to derive a method to simulate random variables, Xi , indexed by i = 1, 2, . . . from an exponential distribution with parameter ? > 0 given a sequence of pseudo-random values Ui from the uniform distribution U(0, 1). [3 marks] (b) Suppose that X1, X2, . . . is a sequence of independent and identically distributed random variables with each random variable Xi having a marginal distribution that is an exponential distribution with parameter ? > 0. Let Sn = Pn i=1 Xi where n is a positive integer and let the random variable N(t) for t > 0 be the number of events in a Poisson Process with parameter ? > 0 that occur in the time interval (0, t). (i) State the probability distribution of N(t). [2 marks] (ii) State a relation between Sn and N(t). [2 marks] (iii) Derive the probability density of the random variable Sn. [6 m

Two hosts are associated with two separate 100 Mbps neighborhood. One is a client's machine with an internet browser, the other is a web server. The organizations are associated by means of a couple of switches and a long stretch, highlight point interface with the following qualities: 640 kbps, 50 ms delay, and a Maximum Packet Size of 1 k bytes. The switches have 8 kbytes of parcel cushion memory. (a) Assuming standard TCP conduct (slow beginning, blockage control, and quick retransmit/recuperation), roughly how long does it require to download a document of 8 Kbytes of information? You might expect that parcel headers and store-and-forward times are inconsequential. You might find it more straightforward to delineate your response with a time-arrangement graph of the bundle trades. [5 marks] (b) How long, around, does it require to download a record of 8 Mbytes from one PC to the next utilizing TCP? [5 marks] (c) Illustrate your response to the past area with a chart showing TCP's conduct over the long run, demonstrating the two significant stages and advances between them. [5 marks] (d) What might happen subjectively assuming the switches had just 4 Kbytes of bundle cushion memory?

(a) Explain the terms Work Conservation and max-min reasonableness, in the specific circumstance of bundle exchanging. [8 marks] (b) Outline the activity of two work-preserving queueing plans that give max-min reasonableness, and two (less difficult) ones that don't. [8 marks] (c) Give something like two principle execution costs related with executions of decency in parcel exchanged switches. [4 marks] 3 Security (a) Describe the Bell-LaPadula security strategy. [6 marks] (b) Describe the Chinese Wall security strategy. [6 marks] (c) To what degree is the Chinese Wall strategy an expansion of Bell-LaPadula? [6 marks] (d) Are both of these arrangements pertinent to computerized privileges the board? [2 marks] 2 CST.2003.7.3 4 Advanced Graphics (a) We need to observe the principal convergence point between an inconsistent beam and a circle of erratic range at an inconsistent situation in space. (I) List and characterize every one of the boundaries expected to determine the calculation of the beam and the circle. [2 marks] (ii) Give a calculation which returns the ideal convergence point (assuming it exists) what's more, the proper ordinary vector at the convergence point. [5 marks] (b) Describe a strategy which changes an erratic circle over to a triangle network at a wanted goal. The ideal goal is determined as an ideal number of triangles, D. Your strategy ought to deliver various triangles, N, which is inside a significant degree of D: D/10 < N < 10D. [4 marks]

Characterize access control records and abilities, and talk about their overall assets and shortcomings. [5 marks] Depict how the entrance control list components work in Unix. [5 marks] You have been approached to construct an assets move framework in which an installment is approved just whenever it has been supported by both a director and a bookkeeper at a bank office. How might you execute this framework utilizing Unix security instruments as the establishment? [10 marks] 6 Data Structures and Algorithms Depict Larsen's technique for dynamic hashing that empowers a record to be found on a circle given its key utilizing only one plate move and just a humble measure of data held in principle memory. [10 marks] In Larsen's technique each key has related pseudo-irregular arrangements of test and signature values. Examine what properties these successions ought to have. Frame an calculation that could be utilized to register the n th test signature pair for guaranteed key. You might accept that the key is a person string. [6 marks] Momentarily examine the reason why Larsen's technique isn't utilized in latest documenting frameworks.

. Compose program to compute straightforward loan cost. Client ought to supply chief sum, loan cost and time 7. Compose program that checks regardless of whether a number is prime. 8

For what reason is MIPS (a large number of guidelines each second) an unfortunate proportion of a PC's execution? [4 marks] Make sense of why superior execution processors use pipelines to expand the MIPS rating but pipelines will generally expand an opportunity to execute a guidance. [4 marks] guidance interpret/execute memory register bring register get access compose back Regarding the exemplary RISC pipeline above, make sense of what an information danger is. [6 marks] How are feed-forward ways used to diminish pipeline slows down?

FIFO, LRU, and CLOCK are three page substitution calculations. (a) Briefly portray the activity of every calculation. [6 marks] (b) The CLOCK technique accepts some equipment support. What might you at some point do to permit the utilization of CLOCK in the event that this equipment support were absent? [2 marks] (c) Assuming great transient territory of reference, which of the over three calculations could you decide to use inside a working framework? How could you not utilize different plans? [2 marks] What is a cushion store? Make sense of why one is utilized, and the way that it works. [6 marks] Which cradle reserve substitution procedure would you decide to use inside an working framework? Legitimize your response. [2 marks] Give two justifications for why the it are different to support prerequisites for network information from those for record framework