ISYE 6644 Midterm Exam 1 - Open Book Section (R) - Part 2 |
Questions and Answers | 2026 Update | 100% Correct - GT. - 118
Questions and Answers Already Graded A+ Premium Exam
Tested And Verified
Subject Area ISYE 6644 Midterm Exam 1 - Open Book Section (R) - Part 2 | Questions and
Answers | 2026 Update | 100% Correct - GT.
Description Comprehensive examination on ISYE 6644 Midterm Exam 1 - Open Book
Section (R) - Part 2 | Questions and Answers | 2026 Update | 100% Correct - GT..
Expected Grade A+
Total Questions 118
Duration 3 hours
Learning Outcomes 1. Demonstrate mastery of core concepts
Accreditation Aligned with US university standards.
Page 1
,Question 1 of 118
In the inverse transform method for generating continuous random variates, if the cumulative
distribution function F(x) is not invertible in closed form, which approach is most appropriate?
A. Use the probability integral transform with numerical root-finding
B. Apply the acceptance-rejection method with a suitable envelope
C. Resort to the Box-Muller transformation
D. Approximate F by a piecewise linear function
The correct answer is:
Correct Action: Apply the acceptance-rejection method with a suitable envelope
Rationales
• Apply the acceptance-rejection method with a suitable envelope (Correct):
This is the correct action. When F is not invertible analytically, numerical inversion is possible but inefficient.
Acceptance-rejection is the standard alternative for distributions without closed-form inverse, as it doesn't require
inversion.
• Use the probability integral transform with numerical root-finding (Incorrect):
This option is not appropriate. Acceptance-rejection is the standard alternative for distributions without closed-form
inverse, as it doesn't require inversion.
• Resort to the Box-Muller transformation (Incorrect):
This option is not appropriate. Acceptance-rejection is the standard alternative for distributions without closed-form
inverse, as it doesn't require inversion.
• Approximate F by a piecewise linear function (Incorrect):
This option is not appropriate. Acceptance-rejection is the standard alternative for distributions without closed-form
inverse, as it doesn't require inversion.
Page 2
,Question 2 of 118
In the batch means method for steady-state simulation output analysis, if the number of batches b is
increased while the total run length n is fixed, the bias in the variance estimator typically:
A. Decreases due to increased independence between batches
B. Increases because each batch becomes shorter and more correlated
C. Remains constant because bias depends only on the batch size
D. Decreases as the square root of b
The correct answer is:
Correct Action: Increases because each batch becomes shorter and more correlated
Rationales
• Increases because each batch becomes shorter and more correlated (Correct):
This is the correct action. With fixed n, increasing b reduces batch size, making batches more correlated (higher
autocorrelation). This increases the bias in the estimator of variance of the sample mean, as the batch means are less
independent.
• Decreases due to increased independence between batches (Incorrect):
This option is not appropriate. This increases the bias in the estimator of variance of the sample mean, as the batch means
are less independent.
• Remains constant because bias depends only on the batch size (Incorrect):
This option is not appropriate. This increases the bias in the estimator of variance of the sample mean, as the batch means
are less independent.
• Decreases as the square root of b (Incorrect):
This option is not appropriate. This increases the bias in the estimator of variance of the sample mean, as the batch means
are less independent.
Page 3
, Question 3 of 118
When comparing two alternative system configurations using simulation, common random numbers
(CRN) are applied to:
A. Reduce variance by inducing positive correlation between the two estimators
B. Reduce variance by inducing negative correlation between the two estimators
C. Eliminate initialization bias by using the same seed
D. Facilitate the use of antithetic variates within each configuration
The correct answer is:
Correct Action: Reduce variance by inducing positive correlation between the two estimators
Rationales
• Reduce variance by inducing positive correlation between the two estimators (Correct):
This is the correct action. CRN uses the same random number streams for both configurations, creating positive correlation
between the sample means. This reduces the variance of the difference estimator, improving the power of comparisons.
• Reduce variance by inducing negative correlation between the two estimators (Incorrect):
This option is not appropriate. This reduces the variance of the difference estimator, improving the power of comparisons.
• Eliminate initialization bias by using the same seed (Incorrect):
This option is not appropriate. This reduces the variance of the difference estimator, improving the power of comparisons.
• Facilitate the use of antithetic variates within each configuration (Incorrect):
This option is not appropriate. This reduces the variance of the difference estimator, improving the power of comparisons.
Page 4
Questions and Answers | 2026 Update | 100% Correct - GT. - 118
Questions and Answers Already Graded A+ Premium Exam
Tested And Verified
Subject Area ISYE 6644 Midterm Exam 1 - Open Book Section (R) - Part 2 | Questions and
Answers | 2026 Update | 100% Correct - GT.
Description Comprehensive examination on ISYE 6644 Midterm Exam 1 - Open Book
Section (R) - Part 2 | Questions and Answers | 2026 Update | 100% Correct - GT..
Expected Grade A+
Total Questions 118
Duration 3 hours
Learning Outcomes 1. Demonstrate mastery of core concepts
Accreditation Aligned with US university standards.
Page 1
,Question 1 of 118
In the inverse transform method for generating continuous random variates, if the cumulative
distribution function F(x) is not invertible in closed form, which approach is most appropriate?
A. Use the probability integral transform with numerical root-finding
B. Apply the acceptance-rejection method with a suitable envelope
C. Resort to the Box-Muller transformation
D. Approximate F by a piecewise linear function
The correct answer is:
Correct Action: Apply the acceptance-rejection method with a suitable envelope
Rationales
• Apply the acceptance-rejection method with a suitable envelope (Correct):
This is the correct action. When F is not invertible analytically, numerical inversion is possible but inefficient.
Acceptance-rejection is the standard alternative for distributions without closed-form inverse, as it doesn't require
inversion.
• Use the probability integral transform with numerical root-finding (Incorrect):
This option is not appropriate. Acceptance-rejection is the standard alternative for distributions without closed-form
inverse, as it doesn't require inversion.
• Resort to the Box-Muller transformation (Incorrect):
This option is not appropriate. Acceptance-rejection is the standard alternative for distributions without closed-form
inverse, as it doesn't require inversion.
• Approximate F by a piecewise linear function (Incorrect):
This option is not appropriate. Acceptance-rejection is the standard alternative for distributions without closed-form
inverse, as it doesn't require inversion.
Page 2
,Question 2 of 118
In the batch means method for steady-state simulation output analysis, if the number of batches b is
increased while the total run length n is fixed, the bias in the variance estimator typically:
A. Decreases due to increased independence between batches
B. Increases because each batch becomes shorter and more correlated
C. Remains constant because bias depends only on the batch size
D. Decreases as the square root of b
The correct answer is:
Correct Action: Increases because each batch becomes shorter and more correlated
Rationales
• Increases because each batch becomes shorter and more correlated (Correct):
This is the correct action. With fixed n, increasing b reduces batch size, making batches more correlated (higher
autocorrelation). This increases the bias in the estimator of variance of the sample mean, as the batch means are less
independent.
• Decreases due to increased independence between batches (Incorrect):
This option is not appropriate. This increases the bias in the estimator of variance of the sample mean, as the batch means
are less independent.
• Remains constant because bias depends only on the batch size (Incorrect):
This option is not appropriate. This increases the bias in the estimator of variance of the sample mean, as the batch means
are less independent.
• Decreases as the square root of b (Incorrect):
This option is not appropriate. This increases the bias in the estimator of variance of the sample mean, as the batch means
are less independent.
Page 3
, Question 3 of 118
When comparing two alternative system configurations using simulation, common random numbers
(CRN) are applied to:
A. Reduce variance by inducing positive correlation between the two estimators
B. Reduce variance by inducing negative correlation between the two estimators
C. Eliminate initialization bias by using the same seed
D. Facilitate the use of antithetic variates within each configuration
The correct answer is:
Correct Action: Reduce variance by inducing positive correlation between the two estimators
Rationales
• Reduce variance by inducing positive correlation between the two estimators (Correct):
This is the correct action. CRN uses the same random number streams for both configurations, creating positive correlation
between the sample means. This reduces the variance of the difference estimator, improving the power of comparisons.
• Reduce variance by inducing negative correlation between the two estimators (Incorrect):
This option is not appropriate. This reduces the variance of the difference estimator, improving the power of comparisons.
• Eliminate initialization bias by using the same seed (Incorrect):
This option is not appropriate. This reduces the variance of the difference estimator, improving the power of comparisons.
• Facilitate the use of antithetic variates within each configuration (Incorrect):
This option is not appropriate. This reduces the variance of the difference estimator, improving the power of comparisons.
Page 4
