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"Please ignore question 2,3,and 12 from""sample problem CN8814.PDF"" and do the rest thanks Document Preview: Ryerson University CN8814 -Network Mathematics and Simulation -Winter 2013 Select Problems 1. Let X be a random variable that represents the percentage of time a computer processor is active in any day. The cumulative density function (CDF) of X is given by FX(x) = K(x2 + 3x)

0 x 1 where K is a constant. (a) What is the value of K? (b) Determine the probability density function (PDF) of X. (c) Calculate the average percentage of time the processor is idle? (d) Let Y be a random variable that represents the percentage of time an external memory is accessed from the computer in any day. Y is modeled as Y = 2X??1. Determine the average percentage of time the memory is accessed. (e) Calculate the variance of Y . 2. In a iPhone assembling factory, a robot installs a single camera in each phone. The camera is randomly picked from one of the three boxes that have cameras from three different makes. Let these boxes be labeled B1

B2 and B3. Assume that the box selection is fair. The probability that the camera is box B1

B2 and B3 is defective is 0.01, 0.03 and 0.05 respectively. (a) What is the probability that the assembled iPhone has a defective camera in it? (b) Given that the iPhone is defective, what is the probability the camera was from manufacturer B1 (i.e., it is from box B1)? (c) If two cameras are installed in an iPhone, what is the probability that the assembled iPhone has no defective camera? 1 3. A node in a network has access to two data links (namely L1 and L2) to send its packets. It uses link L1 with probability p. Link L1 does not queue the transmitted packets (meaning that it always sends the received packets to the next node immediately)

however, L2 queues the packets with probability q (as it serves more than one node). All the packets are sent eventually to the Internet, and then they are received at the end-device and re-assembled according to the protocol. (a) What is the probability that a packet will be delayed (or queued) if p = 0:8 and q =... Attachments: Sample-Proble....pdf MidTerm2013.pdf Jan 27 2014 09:34 AM"

Solution ID:608818 | This paper was updated on 26-Nov-2015

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