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final_fall04_sol

# final_fall04_sol - EE/CPE 345 FINAL EXAM December 2004 1...

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EE/CPE 345 FINAL EXAM – December 2004 1. Consider a linear congruential random number generator with parameters a = 3, m = 16, and c=0. (a) Select the seed X0 = 3, and generate 3 random variables using this generator. (b) What is the period of this generator? Solution: (a) ( ) 0,1,2,... , mod 1 = + = + i m c aX X i i ( ) ( ) ( ) 1 16 mod 0 11 * 3 11 16 mod 0 9 * 3 X 9 16 mod 0 3 * 3 3 2 1 = + = = + = = + = X X (b) P = m/4=4; 2. We have implemented a random number generator that generates exponential random variables with mean 2. We want to verify the correctness of this generator by collecting samples from simulation and building a histogram which will be compared with the exponential distribution, using a chi-square test. (a) Assuming that we select for the histogram a range [0, M], what should be the value of M, such that we will have no more than 10% generated samples that will fall outside the range? (b) Can we use this generator to generate Poisson arrivals for a queue simulation? Explain. What will be the arrival rate in this case? (c) If we are going to estimate this arrival rate (or alternatively the mean of the exponential r.v.) using the samples obtained from the simulation, how many samples we would need in order to have a 2 digit accuracy (assume the standard deviation S =1 )?

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final_fall04_sol - EE/CPE 345 FINAL EXAM December 2004 1...

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