ISYE 6402 MIDTERM PRACTICE
EXAMINATION 2026 QUESTIONS WITH
ANSWERS GRADED A+
◍ Suppose that X~Bern(0.2). What is E[X^3.5]?.
Answer: 0.2
◍ In the simple linear regression model, we lose three degrees of freedom
because of the estimation of the three model parameters β 0 , β 1 , σ 2 ..
Answer: False
◍ 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)?.
Answer: Unif(0,1). Inverse transform theroem.
◍ In a multiple regression model with 7 predicting variables, the sampling
distribution of the estimated variance of the error terms is a chi-squared
distribution with n-8 degrees of freedom..
Answer: True
◍ We can assess the constant variance assumption in linear regression by
plotting the residuals vs. fitted values..
Answer: True
◍ In the context of evaluating a PRN generator, which kinds of statistical tests
are we interested in?.
Answer: Goodness-of-fit tests, independence tests
◍ TRUE or FALSE? The times between nonhomogeneous Poisson(lambda)
arrivals are i.i.d. Exp(lambda)?.
Answer: False. They are independent but the distribution changes as the
arrival rate changes over time.
,◍ Suppose that U1 and U2 are PRNs. Whats the distribution of U1 + U2?.
Answer: Triangular(0,1,2)
◍ TRUE or FALSE? In ARENA< we can use an APPLY module to apply a
change to a customer's graphical representation, e.g., from a blue marble to a
red marble..
Answer: False
◍ YES or NO? Is it ever OK to use the midsquare random number generator?.
Answer: No
◍ The prediction of the response variable has higher uncertainty than the
estimation of the mean response..
Answer: True. We have additional uncertainty from the newness of the
observation (see Unit 3.2.4).
◍ Brownian motion is also known as....
Answer: Wiener process
◍ Let Y^ be the predicted response at x^ . The variance of Y^ given x^
depends on both the value of x^ and the design matrix..
Answer: True (but the wording was confusing, so everyone got credit no
matter what on this question)
◍ TRUE or FALSE? In the process-interaction worldview, at any time the
system may have many entities interacting with each other as they compete
for resources?.
Answer: True
◍ Which high-level simulation modeling approach does ARENA employ?.
Answer: Process-Interaction
◍ Which module/spreadsheet is NOT in the Advanced Process panel?.
Answer: Process Module. This is in the Basic Process panel.
◍ TRUE or FALSE? The convolution method involves sums of random
variables..
Answer: True
, ◍ We cannot estimate a multiple linear regression model if the predicting
variables are linearly independent..
Answer: False (Explanation: linearly dependent)
◍ If U ~ Unif(0,1), what is the distribution of -2ln(U^4)?.
Answer: Exp(1/8)
◍ Suppose the guy on trial is actually guilty but you incorrectly acquit him. So
you've incorrectly accepted the null hypothesis of innocence. What type of
error have you just made - Type I or Type II?.
Answer: Type II - You have incorrectly accepted the null hypothesis of
innocence.
◍ TRUE or FALSE? In Arena, you can find a SEIZE (i) inside a PROCESS
module, (ii) in the Advanced Process template, (iii) in the Primitive Blocks
template..
Answer: True
◍ Suppose you are approximating the solution of a simple differential equation
involving the function f(x), and you appeal to the relation f(x+h) = f(x) +
hf'(x), where h is some "small" number. What is this method called?.
Answer: Euler's Method
◍ In Arena, where would you find the Expression spreadsheet?.
Answer: Advanced Process
◍ Suppose that we have a sequence of n=100 PRN's, and we observe 70 runs
up and down. Using alpha = 0.01, do we ACCEPT or REJECT the null
hypothesis of independence?.
Answer: ACCEPT null hypothesis
◍ Assumption of normality in linear regression is required for confidence
intervals, prediction intervals, and hypothesis testing..
Answer: True
◍ If the p-value of the overall F-test is close to 0, we can conclude all the
predicting variable coefficients are significantly nonzero..
EXAMINATION 2026 QUESTIONS WITH
ANSWERS GRADED A+
◍ Suppose that X~Bern(0.2). What is E[X^3.5]?.
Answer: 0.2
◍ In the simple linear regression model, we lose three degrees of freedom
because of the estimation of the three model parameters β 0 , β 1 , σ 2 ..
Answer: False
◍ 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)?.
Answer: Unif(0,1). Inverse transform theroem.
◍ In a multiple regression model with 7 predicting variables, the sampling
distribution of the estimated variance of the error terms is a chi-squared
distribution with n-8 degrees of freedom..
Answer: True
◍ We can assess the constant variance assumption in linear regression by
plotting the residuals vs. fitted values..
Answer: True
◍ In the context of evaluating a PRN generator, which kinds of statistical tests
are we interested in?.
Answer: Goodness-of-fit tests, independence tests
◍ TRUE or FALSE? The times between nonhomogeneous Poisson(lambda)
arrivals are i.i.d. Exp(lambda)?.
Answer: False. They are independent but the distribution changes as the
arrival rate changes over time.
,◍ Suppose that U1 and U2 are PRNs. Whats the distribution of U1 + U2?.
Answer: Triangular(0,1,2)
◍ TRUE or FALSE? In ARENA< we can use an APPLY module to apply a
change to a customer's graphical representation, e.g., from a blue marble to a
red marble..
Answer: False
◍ YES or NO? Is it ever OK to use the midsquare random number generator?.
Answer: No
◍ The prediction of the response variable has higher uncertainty than the
estimation of the mean response..
Answer: True. We have additional uncertainty from the newness of the
observation (see Unit 3.2.4).
◍ Brownian motion is also known as....
Answer: Wiener process
◍ Let Y^ be the predicted response at x^ . The variance of Y^ given x^
depends on both the value of x^ and the design matrix..
Answer: True (but the wording was confusing, so everyone got credit no
matter what on this question)
◍ TRUE or FALSE? In the process-interaction worldview, at any time the
system may have many entities interacting with each other as they compete
for resources?.
Answer: True
◍ Which high-level simulation modeling approach does ARENA employ?.
Answer: Process-Interaction
◍ Which module/spreadsheet is NOT in the Advanced Process panel?.
Answer: Process Module. This is in the Basic Process panel.
◍ TRUE or FALSE? The convolution method involves sums of random
variables..
Answer: True
, ◍ We cannot estimate a multiple linear regression model if the predicting
variables are linearly independent..
Answer: False (Explanation: linearly dependent)
◍ If U ~ Unif(0,1), what is the distribution of -2ln(U^4)?.
Answer: Exp(1/8)
◍ Suppose the guy on trial is actually guilty but you incorrectly acquit him. So
you've incorrectly accepted the null hypothesis of innocence. What type of
error have you just made - Type I or Type II?.
Answer: Type II - You have incorrectly accepted the null hypothesis of
innocence.
◍ TRUE or FALSE? In Arena, you can find a SEIZE (i) inside a PROCESS
module, (ii) in the Advanced Process template, (iii) in the Primitive Blocks
template..
Answer: True
◍ Suppose you are approximating the solution of a simple differential equation
involving the function f(x), and you appeal to the relation f(x+h) = f(x) +
hf'(x), where h is some "small" number. What is this method called?.
Answer: Euler's Method
◍ In Arena, where would you find the Expression spreadsheet?.
Answer: Advanced Process
◍ Suppose that we have a sequence of n=100 PRN's, and we observe 70 runs
up and down. Using alpha = 0.01, do we ACCEPT or REJECT the null
hypothesis of independence?.
Answer: ACCEPT null hypothesis
◍ Assumption of normality in linear regression is required for confidence
intervals, prediction intervals, and hypothesis testing..
Answer: True
◍ If the p-value of the overall F-test is close to 0, we can conclude all the
predicting variable coefficients are significantly nonzero..
