ISYE 6644 MIDTERM EXAM CORRECT QUESTIONS
AND ANSWERS SURE A+
(
✔✔(8.12) Consider the PRN's U1 = 0.1 , U2 = 0.9 , and U3 = 0.2. Use Kolmogorov-
Smirnov with α = 0.05 to test to see if these numbers are indeed uniform. Do we
ACCEPT (i.e., fail to reject) or REJECT uniformity? - ✔✔Accept. From table, D(α=0.05,
3) = 0.70760. Create ordered sample set: 0.1, 0.2, 0.9. Since the max value of D test is
0.467, then we fail to reject because it is smaller.
✔✔(9.1) TRUE or FALSE? Simulation output (e.g., consecutive customer waiting times)
is almost never i.i.d. normal - and that's a big fat problem! - ✔✔True
✔✔(9.1) We often distinguish between two general types of simulations with regard to
output analysis. What are they called? - ✔✔Finite-horizon and steady-state
✔✔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".
✔✔(9.2) 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.
AND ANSWERS SURE A+
(
✔✔(8.12) Consider the PRN's U1 = 0.1 , U2 = 0.9 , and U3 = 0.2. Use Kolmogorov-
Smirnov with α = 0.05 to test to see if these numbers are indeed uniform. Do we
ACCEPT (i.e., fail to reject) or REJECT uniformity? - ✔✔Accept. From table, D(α=0.05,
3) = 0.70760. Create ordered sample set: 0.1, 0.2, 0.9. Since the max value of D test is
0.467, then we fail to reject because it is smaller.
✔✔(9.1) TRUE or FALSE? Simulation output (e.g., consecutive customer waiting times)
is almost never i.i.d. normal - and that's a big fat problem! - ✔✔True
✔✔(9.1) We often distinguish between two general types of simulations with regard to
output analysis. What are they called? - ✔✔Finite-horizon and steady-state
✔✔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".
✔✔(9.2) 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.
