ISYE 6644 MIDTERM EXAM |
NEWEST EXAM COMPREHENSIVE
QUESTIONS AND VERIFIED
ANSWERS GRADED A+
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
TRUE or FALSE? The time between Poisson(lambda) arrivals are i.i.d.
Exp(lambda). - ✔✔✔ Correct Answer > True. As long as lambda doesn't
change over time.[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
1
,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.
TRUE or FALSE? In Arena, a primitive QUEUE block can connect with
a PROCESS module? - ✔✔✔ Correct Answer > False
TRUE or FALSE? The times between nonhomogeneous Poisson(lambda)
arrivals are i.i.d. Exp(lambda)? - ✔✔✔ Correct Answer > False. They are
independent but the distribution changes as the arrival rate changes over
time.
TRUE or FALSE? In Arena, you can pre-assign a service time as an
attribute before you actually get to the server that you'll be using. -
✔✔✔ Correct Answer > True
TRUE or FALSE? In Arena, the SEIZE, DELAY, RELEASE
functionalities are in multiple templates. - ✔✔✔ Correct Answer > True
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? -
2
, ✔✔✔ Correct Answer >
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.
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.
What is the recommended method to generate nonhomogeneous
Poisson arrivals? - ✔✔✔ Correct Answer > Thinning
Brownian motion is also known as... - ✔✔✔ Correct Answer > Wiener
process
3
NEWEST EXAM COMPREHENSIVE
QUESTIONS AND VERIFIED
ANSWERS GRADED A+
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
TRUE or FALSE? The time between Poisson(lambda) arrivals are i.i.d.
Exp(lambda). - ✔✔✔ Correct Answer > True. As long as lambda doesn't
change over time.[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
1
,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.
TRUE or FALSE? In Arena, a primitive QUEUE block can connect with
a PROCESS module? - ✔✔✔ Correct Answer > False
TRUE or FALSE? The times between nonhomogeneous Poisson(lambda)
arrivals are i.i.d. Exp(lambda)? - ✔✔✔ Correct Answer > False. They are
independent but the distribution changes as the arrival rate changes over
time.
TRUE or FALSE? In Arena, you can pre-assign a service time as an
attribute before you actually get to the server that you'll be using. -
✔✔✔ Correct Answer > True
TRUE or FALSE? In Arena, the SEIZE, DELAY, RELEASE
functionalities are in multiple templates. - ✔✔✔ Correct Answer > True
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? -
2
, ✔✔✔ Correct Answer >
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.
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.
What is the recommended method to generate nonhomogeneous
Poisson arrivals? - ✔✔✔ Correct Answer > Thinning
Brownian motion is also known as... - ✔✔✔ Correct Answer > Wiener
process
3
