ISYE-6644 Simulation Exam Study Questions and
100% Correct Verified Answers
What are i.i.d. random variables? - ✔✔It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the
throws are "independent".
And every throw is 50:50 (heads:tails), so the coin is and stays fair - the distribution from which
every throw is drawn, so to speak, is and stays the same: "identically distributed".
(1.2) TRUE or FALSE? Suppose that X1,X2,...,Xn are consecutive waiting times, and we define the
sample mean X¯=∑Xi/n. Then Var(X¯)=Var(Xi)/n. - ✔✔False. Very FALSE! (The issue is that
correlation between the observations messes up the variance of the sample mean. In fact, this
is one of the main reasons why output analysis is difficult!)
(9.4) TRUE or FALSE? You can also conduct finite-horizon estimation for quantities other than
expected values, e.g., simulate a bank from 8:00 a.m. to 5:00 p.m., and find a confidence
interval for the 95th quantile of customer waiting times. - ✔✔True
(9.5) How can we deal with initialization bias if we want to do a steady-state analysis? -
✔✔Make an extremely long run in order to overwhelm it. Also, Truncate (delete) some of
the initial data.
(9.6) Which scenarios might be well-suited for a steady-state analysis? - ✔✔1) Simulate an
assembly line working 24/7. 2) A Markov chain simulated until the transition probabilities
appear to converge.
(9.6) The method of batch means - ✔✔The resulting batch sample means are aproximately
i.i.d. normal.
(9.7) True or False. The method of batch means is easy to use. - ✔✔True
, (9.7) True or False. Batch means chops the consecutive observations into a number of
nonoverlapping, contiguous batches. - ✔✔True
(9.7) True or False. You can use the method of batch means to obtain a confidence interval for
the steady-state mean μ. - ✔✔True
(9.7) True or False. The batch means estimator for the variance parameter σ^2 is asymptotically
unbiased as the batch size m→∞. - ✔✔True
(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. -
✔✔All. We can get CIs for means, variances, quantiles, and differences between the means
of two systems.
Bernoulli probability selection problem - ✔✔Bunch of Bernoulli populations and find the one
with the best success probability
Multinomial cell selection problem - ✔✔
Normal means ranking and selection problem - ✔✔Bunch of normal distributions and we
want to find the one with the largest or smallest mean.
(10.2) "Assume unknown variance sigma^2". Probably will use t-distribution. - ✔✔True.
(10.2) If we have an i.i.d. normal sample of observations, X1,X2,...,Xn, what probability
distribution is most-commonly used to obtain confidence intervals for the mean? - ✔✔t-
distribution
100% Correct Verified Answers
What are i.i.d. random variables? - ✔✔It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the
throws are "independent".
And every throw is 50:50 (heads:tails), so the coin is and stays fair - the distribution from which
every throw is drawn, so to speak, is and stays the same: "identically distributed".
(1.2) TRUE or FALSE? Suppose that X1,X2,...,Xn are consecutive waiting times, and we define the
sample mean X¯=∑Xi/n. Then Var(X¯)=Var(Xi)/n. - ✔✔False. Very FALSE! (The issue is that
correlation between the observations messes up the variance of the sample mean. In fact, this
is one of the main reasons why output analysis is difficult!)
(9.4) TRUE or FALSE? You can also conduct finite-horizon estimation for quantities other than
expected values, e.g., simulate a bank from 8:00 a.m. to 5:00 p.m., and find a confidence
interval for the 95th quantile of customer waiting times. - ✔✔True
(9.5) How can we deal with initialization bias if we want to do a steady-state analysis? -
✔✔Make an extremely long run in order to overwhelm it. Also, Truncate (delete) some of
the initial data.
(9.6) Which scenarios might be well-suited for a steady-state analysis? - ✔✔1) Simulate an
assembly line working 24/7. 2) A Markov chain simulated until the transition probabilities
appear to converge.
(9.6) The method of batch means - ✔✔The resulting batch sample means are aproximately
i.i.d. normal.
(9.7) True or False. The method of batch means is easy to use. - ✔✔True
, (9.7) True or False. Batch means chops the consecutive observations into a number of
nonoverlapping, contiguous batches. - ✔✔True
(9.7) True or False. You can use the method of batch means to obtain a confidence interval for
the steady-state mean μ. - ✔✔True
(9.7) True or False. The batch means estimator for the variance parameter σ^2 is asymptotically
unbiased as the batch size m→∞. - ✔✔True
(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. -
✔✔All. We can get CIs for means, variances, quantiles, and differences between the means
of two systems.
Bernoulli probability selection problem - ✔✔Bunch of Bernoulli populations and find the one
with the best success probability
Multinomial cell selection problem - ✔✔
Normal means ranking and selection problem - ✔✔Bunch of normal distributions and we
want to find the one with the largest or smallest mean.
(10.2) "Assume unknown variance sigma^2". Probably will use t-distribution. - ✔✔True.
(10.2) If we have an i.i.d. normal sample of observations, X1,X2,...,Xn, what probability
distribution is most-commonly used to obtain confidence intervals for the mean? - ✔✔t-
distribution
