11spring-exam2-key

# 11spring-exam2-key - IE 581 Introduction to Stochastic...

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IE 581 — Introduction to Stochastic Simulation Name ___ < KEY > ___ One page of notes, front and back. Closed book. 60 minutes. 1. True or false. (3 points each) (a) T F Splitting and Russian roulette are methods for generating random variates. (b) T F If a sequence of random numbers are uniformly distributed in two dimensions, then the sequence is truly random. (c) T F If a sequence of random numbers are truly random, then they are uniformly distributed in two dimensions. (d) T F Random-number seeds with a "pattern", such as W 0 = 111111111 should be avoided since they lead to predictable sequences of random numbers. (e) T F Marsaglia’s bound ( k ! m ) 1 /k is the least possible number of hyperplanes through a k dimensional cube when using a linear congruential generator with a period of m . (f) T F If Y d is the sample average of the n observations Y 1 , . . . , Y n , then V( Y d ) = V( Y i ) / n , regardless of whether the observations are independent or normally distributed. 2. (10 points) Explain why the expected number of acceptance-rejection iterations is −∞ t ( x ) dx , where t is the majorizing function. ____________________________________________________________ The explanation could be mathematical, mimicking the proof from class. The explanation could be in words, something as simple as the ratio of the ratio of the area under t to the ratio under the target distribution f ____________________________________________________________ Schmeiser Page 1 of 4 Exam #2, March 29, 2011

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IE 581 — Introduction to Stochastic Simulation Name ___ < KEY > ___ 3. (10 points) Consider the random-number generator
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11spring-exam2-key - IE 581 Introduction to Stochastic...

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