ISYE 6644 - GT COMPREHENSIVE STUDY
GUIDE 2026 FULL QUESTIONS AND
SOLUTIONS GRADED A+
◍ A pack contains 4 blue, 2 red, and 2 green pens. Suppose a pen is drawn at
random from the pack, is replaced, and then the process repeated one more
time (for a total of two draws). What is the probability of first drawing a
blue pen and then a green pen?.
Answer: 1/8
◍ A company that sells plastic covers for CDs, DVDs, and Blu-ray disks
offers 6 different models, which differ from each other according to
measurements for the length and the height. All the covers have the same
thickness. An engineer who works for the company had come up with a nice
table for the joint p.m.f. of two random variables , the height in inches of the
plastic cover sold, and , the length in inches of the plastic cover sold.
Unfortunately, however, he has spilled coffee on it, and now some of the
entries are blurred. Knowing that a CD plastic cover is the only plastic cover
that has a square format, i.e., equal height and length, and this is the only
format in which these CD covers are sold, find the probability that the
company will sell a CD plastic cover..
Answer: 0.12
◍ (10.7) TRUE or FALSE? The antithetic random numbers technique
intentionally induces negative correlation between two runs of the same
system - this allows us to better estimate the mean of the system..
Answer: True
◍ (Lesson 9.1: Introduction to Output Analysis.) Let's run a simulation whose
output is a sequence of daily inventory levels for a particular product. Which
of the following statements is true? a. The consecutive daily inventory levels
, are independent.b. The consecutive daily inventory levels are uncorrelated.c.
The consecutive daily inventory levels are normally distributed.d. The
consecutive daily inventory levels may not be identically distributed..
Answer: d. The consecutive daily inventory levels may not be identically
distributed.
◍ (8.3) What is the expected value of the mean of a Pois(λ) random variable?.
Answer: λ is the mean and the variance
◍ Anithetic Random Numbers Method.
Answer: Used for negative correlation between estimators. Opposite of CRN
◍ Suppose U and V are i.i.d. UNIF(0,1) random variables. Select from the
options below an appropriate expression to generate one realization of an
n-sided die toss. (Recall that x is the "ceiling" or "round up" function.).
Answer: nU cieling
◍ (9.7) True or False. The method of batch means is easy to use..
Answer: True
◍ (Lesson 9.1: Introduction to Output Analysis.) Which of the following
problems might best be characterized by a finite-horizon simulation? a.
Simulating long-term hurricane patternsb. Simulating a manufacturing cell
24/7/365c. Simulating the operations of a bank from 9:00 a.m. until 5:00
p.m.d. Simulating the steady-state distribution of a Markov chain.
Answer: c. Simulating the operations of a bank from 9:00 a.m. until 5:00
p.m.
◍ (8.9) Suppose H0 is true, but you've just rejected it! What have you done?.
Answer: Type I error
◍ Consider a Poisson process with rate LAMBDA = 1/H
R. What is the probability that the time between the 5th and 6th arrivals is
greater than 1 hour?.
Answer: 0.368
◍ Suppose an event occurs. What can happen at that point to the FutureEvent
, List (FEL) ?.
Answer: All of the above.
◍ If X has a mean of 5 and a variance of 2, find Var(20 − 4X)..
Answer: 32
◍ (8.1) M/M/1 queue.
Answer: queue length having a single server.
◍ TRUE or FALSE? If the covariance of and is equal to zero, i.e. COV(X,Y)
= 0, then and must be independent..
Answer: false
◍ Suppose that X and Y are i.i.d. with a mean of −5, a variance of 4, and
Cov(X, Y) = 1. Find Corr(X, Y)..
Answer: 1/4
◍ 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? Suppose the arrival of clients to a bank can be modeled
as a Poisson process with a given hourly rate LAMBD
A. Then the expected number of clients arriving between 10:00-11:00am is
the same as the expected number of clients arriving between 1:00-2:00pm..
Answer: True
◍ (10.12) TRUE or FALSE? Sometimes a single-stage procedure like
Bechhofer's is inefficient. In fact, it's possible to use certain sequential
procedures that take observations one-at-a-time (instead of all at once in a
single stage) to make good selection decisions using fewer observations..
Answer: True
◍ IfX Bern(0.5),findE[12+e3X]IfX Bern(0.5),findE[12+e3X].
Answer: 1+(e3/2)1+(e3/2)
◍ TRUE or FALSE? Simulation can be used to study detailed relations that
might be lost in an analytical or numerical treatment, but it might be very
GUIDE 2026 FULL QUESTIONS AND
SOLUTIONS GRADED A+
◍ A pack contains 4 blue, 2 red, and 2 green pens. Suppose a pen is drawn at
random from the pack, is replaced, and then the process repeated one more
time (for a total of two draws). What is the probability of first drawing a
blue pen and then a green pen?.
Answer: 1/8
◍ A company that sells plastic covers for CDs, DVDs, and Blu-ray disks
offers 6 different models, which differ from each other according to
measurements for the length and the height. All the covers have the same
thickness. An engineer who works for the company had come up with a nice
table for the joint p.m.f. of two random variables , the height in inches of the
plastic cover sold, and , the length in inches of the plastic cover sold.
Unfortunately, however, he has spilled coffee on it, and now some of the
entries are blurred. Knowing that a CD plastic cover is the only plastic cover
that has a square format, i.e., equal height and length, and this is the only
format in which these CD covers are sold, find the probability that the
company will sell a CD plastic cover..
Answer: 0.12
◍ (10.7) TRUE or FALSE? The antithetic random numbers technique
intentionally induces negative correlation between two runs of the same
system - this allows us to better estimate the mean of the system..
Answer: True
◍ (Lesson 9.1: Introduction to Output Analysis.) Let's run a simulation whose
output is a sequence of daily inventory levels for a particular product. Which
of the following statements is true? a. The consecutive daily inventory levels
, are independent.b. The consecutive daily inventory levels are uncorrelated.c.
The consecutive daily inventory levels are normally distributed.d. The
consecutive daily inventory levels may not be identically distributed..
Answer: d. The consecutive daily inventory levels may not be identically
distributed.
◍ (8.3) What is the expected value of the mean of a Pois(λ) random variable?.
Answer: λ is the mean and the variance
◍ Anithetic Random Numbers Method.
Answer: Used for negative correlation between estimators. Opposite of CRN
◍ Suppose U and V are i.i.d. UNIF(0,1) random variables. Select from the
options below an appropriate expression to generate one realization of an
n-sided die toss. (Recall that x is the "ceiling" or "round up" function.).
Answer: nU cieling
◍ (9.7) True or False. The method of batch means is easy to use..
Answer: True
◍ (Lesson 9.1: Introduction to Output Analysis.) Which of the following
problems might best be characterized by a finite-horizon simulation? a.
Simulating long-term hurricane patternsb. Simulating a manufacturing cell
24/7/365c. Simulating the operations of a bank from 9:00 a.m. until 5:00
p.m.d. Simulating the steady-state distribution of a Markov chain.
Answer: c. Simulating the operations of a bank from 9:00 a.m. until 5:00
p.m.
◍ (8.9) Suppose H0 is true, but you've just rejected it! What have you done?.
Answer: Type I error
◍ Consider a Poisson process with rate LAMBDA = 1/H
R. What is the probability that the time between the 5th and 6th arrivals is
greater than 1 hour?.
Answer: 0.368
◍ Suppose an event occurs. What can happen at that point to the FutureEvent
, List (FEL) ?.
Answer: All of the above.
◍ If X has a mean of 5 and a variance of 2, find Var(20 − 4X)..
Answer: 32
◍ (8.1) M/M/1 queue.
Answer: queue length having a single server.
◍ TRUE or FALSE? If the covariance of and is equal to zero, i.e. COV(X,Y)
= 0, then and must be independent..
Answer: false
◍ Suppose that X and Y are i.i.d. with a mean of −5, a variance of 4, and
Cov(X, Y) = 1. Find Corr(X, Y)..
Answer: 1/4
◍ 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? Suppose the arrival of clients to a bank can be modeled
as a Poisson process with a given hourly rate LAMBD
A. Then the expected number of clients arriving between 10:00-11:00am is
the same as the expected number of clients arriving between 1:00-2:00pm..
Answer: True
◍ (10.12) TRUE or FALSE? Sometimes a single-stage procedure like
Bechhofer's is inefficient. In fact, it's possible to use certain sequential
procedures that take observations one-at-a-time (instead of all at once in a
single stage) to make good selection decisions using fewer observations..
Answer: True
◍ IfX Bern(0.5),findE[12+e3X]IfX Bern(0.5),findE[12+e3X].
Answer: 1+(e3/2)1+(e3/2)
◍ TRUE or FALSE? Simulation can be used to study detailed relations that
might be lost in an analytical or numerical treatment, but it might be very
