ISYE 6644 Exam Newest Exam 2026 | All Questions and
Correct Answers | Verified Answers | Simulation and
Modeling for Engineering and Science | Georgia
Institute of Technology
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. Why is
acceptance-rejection a good method to use to generate X? ------------Correct
Answer--------------------Because the c.d.f. of X is very hard to invert.
Unif(0,1) PRNs can be used to generate which of the following random entities? --
----------Correct Answer--------------------Exp(lambda) random variates, Nor(0,1)
random variates, Triangular random variates, Bern(p) random variates,
Nonhomogeneous Poisson processes, and just about anything else.
If X is an Exp(lambda) random variable with c.d.f. F(x) = 1-e^(-lambdax), what's
the distribution of the random variable 1-e^(-lambdaX)? ------------Correct Answer-
-------------------Unif(0,1). Inverse transform theroem.
If U is a Unif(0,1) random variable, what's the distribution of -1/lambda(ln(U))? ----
--------Correct Answer--------------------Exp(lambda)
,If X is a Nor(0,1) random variate, and Φ ( x ) is the Nor(0,1) c.d.f., what is the
distribution of Φ ( X )? ------------Correct Answer--------------------Uniform. By the
inverse transform theorem, Φ ( X ) ~ Unif(0,1).
How would you simulate the sum of two 6-sided dice tosses? ------------Correct
Answer--------------------[6U1] + [6U2]
If U is Unif(0,1), how can we simulate a Geom(0.6) random variate? ------------
Correct Answer--------------------[ln(U)/ln(0.4)] or [ln(1-U)/ln(0.4)]
Suppose that U and V are PRNs. Let X=U+V. Simulate this 5000 times, and draw a
histogram of the 5000 numbers. What p.d.f. does the histogram look like? ----------
--Correct Answer--------------------Triangular.
In general, the majorizing function t(x) is itself a p.d.f. f(x)? ------------Correct
Answer--------------------False
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. What's a
good method that you can use to generate a realization of X? ------------Correct
Answer--------------------Acceptance-Rejection
, Consider four observations from some unknown distribution, X1=1.5, X2 = -3.7,
X3=2.7, and X4= 0.6. What is the fourth order statistic, denoted X(4)? ------------
Correct Answer--------------------2.7. X(4) means the largest of the sample of 4
observations.
Which of the following are true? ------------Correct Answer--------------------The
closer the majorizing function t(x) is to the true p.d.f. f(x), the more efficient the
A-R algorithm is; h(y) = t(y)/integral of t(x) is itself a p.d.f., random variates from
h(y) should be "easy" to generate
Suppose that an airline can experience three types of departure delays - A, B, and
C, which occur with probabilities 0.4, 0.1, and 0.5, respectively. Delays A, B, and C
are exponential, normal, and Weibull, respectively. YES or NO? Would the
composition method be a good choice to generate a delay time for this scenario?
------------Correct Answer--------------------Yes. Composition would be much more
efficient than figuring out and delaying with the crazy c.d.f. of the overall delay.
Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of (H,W)? ------------Correct Answer--------------------
Bivariate normal distribution with positive correlation coefficient.
The multivariate normal distribution's covariance matrix sigma can be
decomposed into the form sigma = CC^T. What does the C informally stand for? --
----------Correct Answer--------------------Cholesky
Correct Answers | Verified Answers | Simulation and
Modeling for Engineering and Science | Georgia
Institute of Technology
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. Why is
acceptance-rejection a good method to use to generate X? ------------Correct
Answer--------------------Because the c.d.f. of X is very hard to invert.
Unif(0,1) PRNs can be used to generate which of the following random entities? --
----------Correct Answer--------------------Exp(lambda) random variates, Nor(0,1)
random variates, Triangular random variates, Bern(p) random variates,
Nonhomogeneous Poisson processes, and just about anything else.
If X is an Exp(lambda) random variable with c.d.f. F(x) = 1-e^(-lambdax), what's
the distribution of the random variable 1-e^(-lambdaX)? ------------Correct Answer-
-------------------Unif(0,1). Inverse transform theroem.
If U is a Unif(0,1) random variable, what's the distribution of -1/lambda(ln(U))? ----
--------Correct Answer--------------------Exp(lambda)
,If X is a Nor(0,1) random variate, and Φ ( x ) is the Nor(0,1) c.d.f., what is the
distribution of Φ ( X )? ------------Correct Answer--------------------Uniform. By the
inverse transform theorem, Φ ( X ) ~ Unif(0,1).
How would you simulate the sum of two 6-sided dice tosses? ------------Correct
Answer--------------------[6U1] + [6U2]
If U is Unif(0,1), how can we simulate a Geom(0.6) random variate? ------------
Correct Answer--------------------[ln(U)/ln(0.4)] or [ln(1-U)/ln(0.4)]
Suppose that U and V are PRNs. Let X=U+V. Simulate this 5000 times, and draw a
histogram of the 5000 numbers. What p.d.f. does the histogram look like? ----------
--Correct Answer--------------------Triangular.
In general, the majorizing function t(x) is itself a p.d.f. f(x)? ------------Correct
Answer--------------------False
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. What's a
good method that you can use to generate a realization of X? ------------Correct
Answer--------------------Acceptance-Rejection
, Consider four observations from some unknown distribution, X1=1.5, X2 = -3.7,
X3=2.7, and X4= 0.6. What is the fourth order statistic, denoted X(4)? ------------
Correct Answer--------------------2.7. X(4) means the largest of the sample of 4
observations.
Which of the following are true? ------------Correct Answer--------------------The
closer the majorizing function t(x) is to the true p.d.f. f(x), the more efficient the
A-R algorithm is; h(y) = t(y)/integral of t(x) is itself a p.d.f., random variates from
h(y) should be "easy" to generate
Suppose that an airline can experience three types of departure delays - A, B, and
C, which occur with probabilities 0.4, 0.1, and 0.5, respectively. Delays A, B, and C
are exponential, normal, and Weibull, respectively. YES or NO? Would the
composition method be a good choice to generate a delay time for this scenario?
------------Correct Answer--------------------Yes. Composition would be much more
efficient than figuring out and delaying with the crazy c.d.f. of the overall delay.
Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of (H,W)? ------------Correct Answer--------------------
Bivariate normal distribution with positive correlation coefficient.
The multivariate normal distribution's covariance matrix sigma can be
decomposed into the form sigma = CC^T. What does the C informally stand for? --
----------Correct Answer--------------------Cholesky
