ISYE 6644 FINAL EXAM NEWEST 2024
COMPLETE 200 QUESTIONS AND CORRECT
DETAILED ANSWERS (VERIFIED
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Suppose we want to estimate the expected average waiting time
(in minutes) for the first m = 100 customers at a bank. We make
r = 3 independent replications of the system, each initialized
empty and idle and consisting of 100 waiting times. The
resulting replicate means are: 12, 14, 11. Find a 95% two-sided
confidence interval for the mean average waiting time for the
first 100 customers. - ANSWER- [8.5, 16.1]
Suppose that µ ∈ [−30, 90] is a 90% confidence interval for the
mean cost incurred by a certain inventory policy. Further
suppose that this interval was based on 4 independent
replications of the underlying inventory system. Unfortunately,
the boss has decided that she wants a 95% confidence interval.
Can you supply it? - ANSWER- [−51.14, 111.14].
,2|Page
TRUE or FALSE? Welch's method is a graphical technique to
estimate truncation (initialization bias) points for steady-state
simulation. - ANSWER- True
Suppose that we're studying a stochastic process whose
covariance function is Rk = 3−k for k = 0, ±1, ±2, and 0
otherwise. Find the variance of X¯ 3 (the sample mean of the
first 3 observations). - ANSWER- 2.11
Consider the following 5 observations: 54 80 75 62 90 If we
choose a batch size of 3, calculate all of the overlapping batch
means for me. - ANSWER- 69.7, 72.3, 75.7
Which variance reduction method uses the difference X¯ − Y¯
of two positively correlated sample means to get a lower-
variance estimator for the difference µX − µY of the underlying
unknown means? - ANSWER- Common random numbers.
Which variance reduction method most-closely resembles
regression, e.g., an estimator for the expected value E[X] of the
form Y = X¯ − β(C − E[C]), where E[C] is known and β is a
constant, so that Y is unbiased for E[X]. - ANSWER- Control
variates
,3|Page
TRUE or FALSE? 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!
Suppose we are interested in determining which of 3 soft drinks
is most likely to be chosen by a person in a survey. Which type
of ranking-and-selection problem is this? - ANSWER-
Multinomial
TRUE or FALSE? Sequential ranking-and-selection procedures
are designed to stop early if one alternative seems to be way out
in front of the others. - ANSWER- TRUE
Suppose, when designing a ranking-and-selection procedure,
you have decided to increase the desired probability of correct
selection compared to a previous run of the procedure. What can
you expect? - ANSWER- Larger sample sizes
TRUE or FALSE? The runs "up and down" test is most often
used to test for goodness-of-fit of observations. - ANSWER-
FALSE. It's a test for independence.
, 4|Page
Draw an Arena DECIDE module. - ANSWER- It's a sideways
diamond.
In what Arena template would you find the Sequence
spreadsheet? - ANSWER- Advanced Transfer
In Arena, what module can you use to merge multiple entities
into one? - ANSWER- Batch
TRUE or FALSE? Suppose that U1, U2, . . . are truly i.i.d.
U(0,1) random variables. Then a 95% chi-square goodness-of-fit
test for uniformity will incorrectly reject uniformity of the
observations about 5% of the tim - ANSWER- TRUE (that's
what Type I error is.)
TRUE or FALSE? Suppose Z1, . . . , Z6 are i.i.d. standard
normal random variables obtained by the Box-Muller method.
Then P6 i=1 Z 2 i ∼ Erlang3(1/2). - ANSWER- TRUE. The sum
of 6 i.i.d. Z 2 i random variables is a χ 2 (6), which is itself an
Erlang3(1/2).
If U, V are i.i.d. U(0,1), what's the distribution of −ln(√ U) −
ln(√ V )? - ANSWER- −ln(√ U) − ln(√ V ) = −1/2ln(U) − 1
/2ln(V ) ∼ Erlang2(2).
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