11spring-exam1-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 By definition of simulation input , we do not know its distribution. (b) T F A sample quantile is an example of a sample mean. (c) T F A point estimator is a function of the simulation output. (d) T F If the simulation output are independent and identically distributed, then the usual estimator of the standard error of the point estimator θ ˆ is Y d (1 Y d ) / ( n 1). (e) T F When using the inverse transformation to generate random variates, exactly one random number u always is used to generate one random variate x . (f) T F Either x = −μ ln(1 u ) or x = −μ ln( u ) is the inverse transformation method for generating exponential random variates with mean μ . (g) T F The method of macro/micro replications is used to obtain improved point estimators. (h) T F When using antithetic variates, Θ ˆ = ( Θ ˆ A + Θ ˆ B ) / 2, we hope to induce negative correlation between Θ ˆ A and Θ ˆ B so that V( Θ ˆ A ) and V( Θ ˆ B ) will be reduced. (i) T F When using common random numbers to compare θ A to θ B , we hope to induce positive correlation between Θ ˆ A and Θ ˆ B so that V( Θ ˆ A ) and V( Θ ˆ B ) will be reduced. (j) T F In terms of the sample average, the number of independent observations equivalent to n dependent observations is n / γ 0 , where γ 0 is the sum of all autocorrelations. 2. Consider steady-state normal AR(1) data Y i + 1 = μ Y + α ( Y i − μ Y ) + ε i + 1 . Let Y d denote the sample average of Y 1 , Y 2 , . . . , Y n . (a) (3 points) T F
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11spring-exam1-key - IE 581 Introduction to Stochastic...

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