ISYE 6644 OH EXAM / ACTUAL ISYE 6644 OH EXAM 1 LATEST
2026/2027 PRACTICE QUESTIONS AND A NEW UPDATED STUDY
GUIDE ACCURATE EXAM APPROVED QUESTIONS AND CORRECT
DETAILED SOLUTIONS WITH RATIONALES (100% CORRECT
VERIFIED ANSWERS) CURRENTLY UPDATED VERSION 2026
EDITION |GUARANTEED PASS A+ (BRAND NEW!) FULL REVISED
ISYE 6644 OH APPROVED EXAM 1
Question 1
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of
customers showing up is greater than the service rate of the single-server, then a
long queue will only rarely be formed.
A) TRUE
B) FALSE
Correct Answer: B) FALSE
Rationale: In queueing theory, the traffic intensity is defined as ρ = λ/μ. When λ
> μ (arrival rate exceeds service rate), ρ > 1, meaning the system is unstable and
the queue length will grow without bound over time. Long queues will form
frequently, not rarely. This is a fundamental concept in M/M/1 queue analysis
and a critical condition for system stability .
Question 2
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of
customers showing up is less than the service rate of the single-server, then the
queue will not explode to infinity.
A) TRUE
,B) FALSE
Correct Answer: A) TRUE
Rationale: When λ < μ, the traffic intensity ρ < 1, which represents the stability
condition for a single-server queue. The system reaches a steady-state
distribution where the queue length does not grow without bound. This is a
necessary condition for the existence of a stationary distribution in an M/M/1
queue system .
Question 3
Consider a family that has 2 children. Assume that P(kid is a boy) = 1/3 and P(kid
is a girl) = 2/3, and that the genders of the 2 kids are independent. What is the
probability that both kids are girls given that we know at least 1 of them is a girl?
A) 1/16
B) 1/8
C) 1/5
D) 1/4
E) 1/2
Correct Answer: E) 1/2
Rationale: The sample space is S = {GG, GB, BG, BB} with probabilities: P(GG)
= (2/3)(2/3) = 4/9, P(GB) = (2/3)(1/3) = 2/9, P(BG) = (1/3)(2/3) = 2/9, P(BB) =
(1/3)(1/3) = 1/9. Let A be the event that both are girls = {GG}, and B be the event
that at least one is a girl = {GG, GB, BG}. Then P(A|B) = P(A∩B)/P(B) =
(4/9)/(4/9 + 2/9 + 2/9) = (4/9)/(8/9) = 1/2 .
,Question 4
TRUE or FALSE? Discrete-event simulations are particularly suitable for
analyzing continuous-flow phenomena such as weather patterns propagating across
the country.
A) TRUE
B) FALSE
Correct Answer: B) FALSE
Rationale: Discrete-event simulations are designed for systems where state changes
occur at discrete points in time (events). Continuous-flow phenomena like weather
patterns are better modeled using continuous simulation approaches or system
dynamics. Discrete-event simulation is most appropriate for systems involving
queues, inventories, and processes with distinct events .
Question 5
The planet Tranya has 240-day years. Suppose there are three Tranyanians in the
room. What is the probability that at least two of them share the same birthday?
A) 0.0125
B) 0.025
C) 0.035
D) 0.149
E) 0.9975
Correct Answer: A) 0.0125
, Rationale: P(none share the same birthday) = (240 × 239 × 238) / 240^3 = 0.9875.
Therefore, P(at least two share a birthday) = 1 - P(none share) = 1 - 0.9875 =
0.0125. This is the complement probability approach commonly used in birthday
problem calculations .
Question 6
TRUE or FALSE? The function f(x) = 5e^(-5x) for x ≥ 0 is a valid probability
density function.
A) TRUE
B) FALSE
Correct Answer: A) TRUE
Rationale: For f(x) to be a valid pdf, it must be non-negative and integrate to 1 over
its support. ∫₀^∞ 5e^(-5x) dx = [-e^(-5x)]₀^∞ = 0 - (-1) = 1. This represents an
exponential distribution with rate λ = 5, which is a valid probability density
function .
Question 7
The exponential distribution has the memoryless property. Which of the following
statements best describes this property for X ~ Exp(λ)?
A) P(X > s + t) = P(X > s) × P(X > t) for all s, t > 0
B) P(X > s + t | X > s) = P(X > t) for all s, t > 0
C) P(X ≤ s + t) = P(X ≤ s) + P(X ≤ t) for all s, t > 0
D) P(X = s + t) = P(X = s) × P(X = t) for all s, t > 0
E) None of the above
2026/2027 PRACTICE QUESTIONS AND A NEW UPDATED STUDY
GUIDE ACCURATE EXAM APPROVED QUESTIONS AND CORRECT
DETAILED SOLUTIONS WITH RATIONALES (100% CORRECT
VERIFIED ANSWERS) CURRENTLY UPDATED VERSION 2026
EDITION |GUARANTEED PASS A+ (BRAND NEW!) FULL REVISED
ISYE 6644 OH APPROVED EXAM 1
Question 1
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of
customers showing up is greater than the service rate of the single-server, then a
long queue will only rarely be formed.
A) TRUE
B) FALSE
Correct Answer: B) FALSE
Rationale: In queueing theory, the traffic intensity is defined as ρ = λ/μ. When λ
> μ (arrival rate exceeds service rate), ρ > 1, meaning the system is unstable and
the queue length will grow without bound over time. Long queues will form
frequently, not rarely. This is a fundamental concept in M/M/1 queue analysis
and a critical condition for system stability .
Question 2
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of
customers showing up is less than the service rate of the single-server, then the
queue will not explode to infinity.
A) TRUE
,B) FALSE
Correct Answer: A) TRUE
Rationale: When λ < μ, the traffic intensity ρ < 1, which represents the stability
condition for a single-server queue. The system reaches a steady-state
distribution where the queue length does not grow without bound. This is a
necessary condition for the existence of a stationary distribution in an M/M/1
queue system .
Question 3
Consider a family that has 2 children. Assume that P(kid is a boy) = 1/3 and P(kid
is a girl) = 2/3, and that the genders of the 2 kids are independent. What is the
probability that both kids are girls given that we know at least 1 of them is a girl?
A) 1/16
B) 1/8
C) 1/5
D) 1/4
E) 1/2
Correct Answer: E) 1/2
Rationale: The sample space is S = {GG, GB, BG, BB} with probabilities: P(GG)
= (2/3)(2/3) = 4/9, P(GB) = (2/3)(1/3) = 2/9, P(BG) = (1/3)(2/3) = 2/9, P(BB) =
(1/3)(1/3) = 1/9. Let A be the event that both are girls = {GG}, and B be the event
that at least one is a girl = {GG, GB, BG}. Then P(A|B) = P(A∩B)/P(B) =
(4/9)/(4/9 + 2/9 + 2/9) = (4/9)/(8/9) = 1/2 .
,Question 4
TRUE or FALSE? Discrete-event simulations are particularly suitable for
analyzing continuous-flow phenomena such as weather patterns propagating across
the country.
A) TRUE
B) FALSE
Correct Answer: B) FALSE
Rationale: Discrete-event simulations are designed for systems where state changes
occur at discrete points in time (events). Continuous-flow phenomena like weather
patterns are better modeled using continuous simulation approaches or system
dynamics. Discrete-event simulation is most appropriate for systems involving
queues, inventories, and processes with distinct events .
Question 5
The planet Tranya has 240-day years. Suppose there are three Tranyanians in the
room. What is the probability that at least two of them share the same birthday?
A) 0.0125
B) 0.025
C) 0.035
D) 0.149
E) 0.9975
Correct Answer: A) 0.0125
, Rationale: P(none share the same birthday) = (240 × 239 × 238) / 240^3 = 0.9875.
Therefore, P(at least two share a birthday) = 1 - P(none share) = 1 - 0.9875 =
0.0125. This is the complement probability approach commonly used in birthday
problem calculations .
Question 6
TRUE or FALSE? The function f(x) = 5e^(-5x) for x ≥ 0 is a valid probability
density function.
A) TRUE
B) FALSE
Correct Answer: A) TRUE
Rationale: For f(x) to be a valid pdf, it must be non-negative and integrate to 1 over
its support. ∫₀^∞ 5e^(-5x) dx = [-e^(-5x)]₀^∞ = 0 - (-1) = 1. This represents an
exponential distribution with rate λ = 5, which is a valid probability density
function .
Question 7
The exponential distribution has the memoryless property. Which of the following
statements best describes this property for X ~ Exp(λ)?
A) P(X > s + t) = P(X > s) × P(X > t) for all s, t > 0
B) P(X > s + t | X > s) = P(X > t) for all s, t > 0
C) P(X ≤ s + t) = P(X ≤ s) + P(X ≤ t) for all s, t > 0
D) P(X = s + t) = P(X = s) × P(X = t) for all s, t > 0
E) None of the above
