Quiz Solutions

Topics: Normal distribution, Cumulative distribution function, Random variable Pages: 3 (261 words) Published: February 10, 2013
Student Name:

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Student #:

Carleton University
Department ofSystems and Computer Engineering SYSC4005/5001 Discrete-Event Simulation, In class quiz January 28 2013, 6:00pm-6:30pm a) Packets arrive at a processing facility that has two processors, a slow one and a fast one; packets are routed to the slow processor with probability 2/3 and in this case they experience a delay that is an exponentially distributed random variable with mean 3ms. However, when packets are routed to the fast processor they experience a constant processing delay of Ims. a) (4 points) Derive and plot the cumulative distribution function and the probability density ofthe packet delay and b) (2 points) calculate its mean ~ value. c) (4 points) You collect the following packet delay measurements: 3,4,1,2,2,3 ms. Estimate how a '\ many additional samples you should collect so that the 90% confidence interval of the mean delay is +1........ O.lms around the sample mean (assume that the sample standard deviation wont change appreciably!) Za

packet '--_.....



Slow processor -mean delay 3ms Fast processor- constant delay

For the standard nonna! distribution note that:


2.525, Z0025


1.645, ZOI'" 1.285



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J ~r;)J7( = J'"X




-1 1


.:: 2.33"" >.

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