ISYE 6644 OAN 1 SIMULATION
COMPREHENSIVE STUDY GUIDE 2026 FULL
QUESTIONS AND SOLUTIONS GRADED A+
◍ Suppose there are 3 people in the line called joe.queue and 5 people in the
line called tom.queue. What is the value of the following Arena
expression?(NQ(joe.queue) > NQ(tom.queue)) + (TNOW >= 0.
Answer: The logical expression (NQ(joe.queue) > NQ(tom.queue)) is false
(because 3 ≤ 5) and therefore 0. The logical expression (TNOW >= 0) is
always true (since time is always at least 0) and therefore 1. Thus, 0 + 1 = 1
◍ (8.10/8.11) The test statistic is χ0^2 = 9.12. Now, let's use our old friend α =
0.05 in our test. Let k = 4 denote the number of cells (that we ultimately
ended up with) and let s = 1 denote the number of parameters we had to
estimate. Then we compare against χ^2(α=0.05 , k − s − 1) = χ^2(α=0.05 , 2)
= 5.99. Do we ACCEPT (i.e., fail to reject) or REJECT the Geometric
hypothesis?.
Answer: Reject. The test statistic 9.12 is not less than 5.99.
◍ (10.1) Which of the following parameters can you get confidence intervals
for? Means, Variances, Quantiles, Differences between the means of two
systems, or all of those..
Answer: All. We can get CIs for means, variances, quantiles, and differences
between the means of two systems.
◍ (8.8) Suppose that we observe X1 = 5, X2 = 9, and X3 = 1. What's the
method of moments estimate of E[X^2]?.
Answer: 35.6667. Second moment is the sum of the squared samples divided
by the number of samples. (5^2 + 9^2 + 1^2) / 3 = 35.666666667
◍ If you are using a ranking-and-selection procedure and two competitors
, happen to fall within the indifference-zone, then you don't really care too
much which one you end up selecting..
Answer: TRUE. That's why it's called the IZ!
◍ (8.3) What is the expected value of the mean of a Pois(λ) random variable?.
Answer: λ is the mean and the variance
◍ TRUE or FALSE? The square root of the sample variance is unbiased for
the standard deviation.
Answer: FALSE. (E[S 2 ] = σ 2 ; E[S] = σ.)
◍ Normal means ranking and selection problem.
Answer: Bunch of normal distributions and we want to find the one with the
largest or smallest mean.
◍ TRUE or FALSE? The acceptance-rejection's majorizing function t(x) is
usually a p.d.f..
Answer: FALSE. (It integrates to something > 1.)
◍ (8.9) Suppose H0 is true, but you've just rejected it! What have you done?.
Answer: Type I error
◍ (10.2) "Assume unknown variance sigma^2". Probably will use
t-distribution..
Answer: True.
◍ Find x such that e 2x = 1/x. (Get within two decimals).
Answer: Bisection search quickly reveals that x is about 0.4265
◍ TRUE or FALSE? In Arena, an alternative expression to generate
exponential interarrival times having a mean of 3 is -(1/3)*LN(UNIF(0,1)).
Answer: FALSE. This is the Inverse Transform Method to generate an
observation coming from Exp(λ = 3), which has a mean of 1/3.
◍ (9.7) True or False. The batch means estimator for the variance parameter
σ^2 is asymptotically unbiased as the batch size m→∞..
Answer: True
◍ (9.6) Which scenarios might be well-suited for a steady-state analysis?.
COMPREHENSIVE STUDY GUIDE 2026 FULL
QUESTIONS AND SOLUTIONS GRADED A+
◍ Suppose there are 3 people in the line called joe.queue and 5 people in the
line called tom.queue. What is the value of the following Arena
expression?(NQ(joe.queue) > NQ(tom.queue)) + (TNOW >= 0.
Answer: The logical expression (NQ(joe.queue) > NQ(tom.queue)) is false
(because 3 ≤ 5) and therefore 0. The logical expression (TNOW >= 0) is
always true (since time is always at least 0) and therefore 1. Thus, 0 + 1 = 1
◍ (8.10/8.11) The test statistic is χ0^2 = 9.12. Now, let's use our old friend α =
0.05 in our test. Let k = 4 denote the number of cells (that we ultimately
ended up with) and let s = 1 denote the number of parameters we had to
estimate. Then we compare against χ^2(α=0.05 , k − s − 1) = χ^2(α=0.05 , 2)
= 5.99. Do we ACCEPT (i.e., fail to reject) or REJECT the Geometric
hypothesis?.
Answer: Reject. The test statistic 9.12 is not less than 5.99.
◍ (10.1) Which of the following parameters can you get confidence intervals
for? Means, Variances, Quantiles, Differences between the means of two
systems, or all of those..
Answer: All. We can get CIs for means, variances, quantiles, and differences
between the means of two systems.
◍ (8.8) Suppose that we observe X1 = 5, X2 = 9, and X3 = 1. What's the
method of moments estimate of E[X^2]?.
Answer: 35.6667. Second moment is the sum of the squared samples divided
by the number of samples. (5^2 + 9^2 + 1^2) / 3 = 35.666666667
◍ If you are using a ranking-and-selection procedure and two competitors
, happen to fall within the indifference-zone, then you don't really care too
much which one you end up selecting..
Answer: TRUE. That's why it's called the IZ!
◍ (8.3) What is the expected value of the mean of a Pois(λ) random variable?.
Answer: λ is the mean and the variance
◍ TRUE or FALSE? The square root of the sample variance is unbiased for
the standard deviation.
Answer: FALSE. (E[S 2 ] = σ 2 ; E[S] = σ.)
◍ Normal means ranking and selection problem.
Answer: Bunch of normal distributions and we want to find the one with the
largest or smallest mean.
◍ TRUE or FALSE? The acceptance-rejection's majorizing function t(x) is
usually a p.d.f..
Answer: FALSE. (It integrates to something > 1.)
◍ (8.9) Suppose H0 is true, but you've just rejected it! What have you done?.
Answer: Type I error
◍ (10.2) "Assume unknown variance sigma^2". Probably will use
t-distribution..
Answer: True.
◍ Find x such that e 2x = 1/x. (Get within two decimals).
Answer: Bisection search quickly reveals that x is about 0.4265
◍ TRUE or FALSE? In Arena, an alternative expression to generate
exponential interarrival times having a mean of 3 is -(1/3)*LN(UNIF(0,1)).
Answer: FALSE. This is the Inverse Transform Method to generate an
observation coming from Exp(λ = 3), which has a mean of 1/3.
◍ (9.7) True or False. The batch means estimator for the variance parameter
σ^2 is asymptotically unbiased as the batch size m→∞..
Answer: True
◍ (9.6) Which scenarios might be well-suited for a steady-state analysis?.
