ISYE6644 MIDTERM 2 QUESTIONS AND ANSWERS 2025

ISYE6644 MIDTERM 2 LATEST

If the random variable X has p.d.f. f(x) = 3x^2, for 0<=x<=1, what is the
distribution of the slightly nasty random variable X^3? - ANSWERS-Uniform



Suppose that U and V are i.i.d. Unif(0,1) random variables. How would you
simulate the sum of two 6-sided dice tosses? - ANSWERS-[6U]+[6V]



Suppose that X~Bern(0.2). What is E[X^3.5]? - ANSWERS-0.2



TRUE or FALSE? Let X denote the number of tails from two fair coin tosses.
Then the probability mass function for Y=X^2-1 is:

P(Y=y) = {1/4, if y=-1; 1/2, if y=0; 1/4, if y=1} - ANSWERS-False



YES or NO? Suppose X and Y are random variables that have joint p.d.f. f(x,y) =
c(x+y) for 0<=x<=1 and 0<=y<=1, where c is the constant that makes this integrate
to 1. Are X and Y independent? - ANSWERS-No



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? - ANSWERS-Euler's
Method



TRUE or FALSE? As crazy as it sounds, the Unif(0,1) random numbers generated
on a computer are actually deterministic. - ANSWERS-True
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, ISYE6644 MIDTERM 2 LATEST

If x and y are two consecutive event times in a discrete simulation model, what can
happen during the time interval x<t<y? - ANSWERS-Nothing can happen.



In the course of a simulation study, we should stop to ask "Does our simulation
model correctly mimic the real-world system under study?" What step of the
simulation study process is this? - ANSWERS-Validation



TRUE or FALSE? A fixed-increment simulation clock is well-suited for
simulations that model continuous-time systems such as the movement of an
approaching weather system. - ANSWERS-True



Which high-level simulation modeling approach does ARENA employ? -
ANSWERS-Process-Interaction



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?
- ANSWERS-True



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. -
ANSWERS-False



TRUE or FALSE? In Arena, the Schedule spreadsheet can be used to establish
either resource capacity schedules or arrival rate schedules. - ANSWERS-True
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, ISYE6644 MIDTERM 2 LATEST

In Arena, what typically happens when you do not RELEASE a SEIZE'd resource?
- ANSWERS-A long line forms in front of the resource.



TRUE or FALSE? An Arena ASSIGN module can be used to assign values to
attributes AND variables? - ANSWERS-True



Suppose U1, U2, U3, U4 are i.i.d. Unif(0,1). What is the probability that we will
see exactly 1 run up and run down? - ANSWERS-1/12



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? - ANSWERS-ACCEPT null hypothesis



We are testing a certain COVID vaccine. Our null hypothesis is the assumption
that the vaccine is safe. If we accept this null hypothesis but the medication is
actually harmful, what type of error have we committed? - ANSWERS-Type II
error



From the convolutions, select the statement that is incorrect. - ANSWERS-The
sum of 5 i.i.d. Pois(3) RVs is Exp(15)



TRUE or FALSE? In a single-server queue simulation, if the arrival rate of
customers showing up is many times higher than the service rate of the single-
server, then a queue will not be formed. - ANSWERS-False
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