ISYE6644/ ISYE 6644 MIDTERM EXAM
NEWEST ACTUAL EXAM WITH COMPLETE
QUESTIONS AND DETAILED ANSWERS
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Graphically, what is an indication that your pseudorandom
number generator is "no good" (M1L7). - ✔✔✔ Correct Answer
> Example was graphing two "random variates" in the x-y plane
that were generated from uniform distributions transformed
into normal distr (Box Muller Method). If a pattern in the graph
appears, this is "bad." You expect lots of random points
clustered around the center that spread out evenly in all
directions from the center. Spiral patterns = no good.
In Queuing models, what does each part of the Kendall notation
mean: A/B/C (general version) applied to a M/M/1 (a specific
version)(M1L7)? - ✔✔✔ Correct Answer > A = Distrib of arrival
times
B = Distrib. of service times
C = # of servers in the system
M = arrival times are Poisson process (lambda)
,M = exponential service times (mu)
1 = a single server
"M" stands for Markov, but really it means exponential?
Describe what a "random walk" model is and what "motion" it
converges to (M1L7)? - ✔✔✔ Correct Answer > Model where
the variable "step" size changes randomly with each time
increment (step size = randomly sampled from a normal
distribution?).
Converges to Brownian Motion: as time steps become smaller
and # of steps larger. Continuous time, stochastic.
Random samples from which distribution can be transformed
into random variables of any other distribution (M1L8)? - ✔✔✔
Correct Answer > Uniform (0, 1)
What specific pseudorandom number generating algorithm was
covered in detail in Module 1? It involves choosing a seed
value, two carefully chosen constants a and m, using the
modulus operator, and then normalizing all values to fit
,between 0 and 1 by dividing by m (M1L8). - ✔✔✔ Correct
Answer > Linear Congruential Generator (LCG).
The Desert Island Generator is is an LCG with a=16807 and m =
2^31 - 1 (a very large prime number.
X(i) = 16807X(i - 1) mod (2^31 - 1)
U(i) = X(i) / m
What are the 3 general steps for the inverse transform method
(M1L8)? - ✔✔✔ Correct Answer > 1. Generate the Unif (0, 1)
PRN (U_i)
2. For the desired probability distribution, get the inverse of its
CDF (F^-1(U_i)). This involves setting the CDF (F(X)) equal to U,
and then solving for X (X will by F^-1(U), a function of U).
3. Plugging in U values from #1 into #2, gets a random variable
from the desired distribution!
Which probability distribution does the following approximate:
-(1/lamba)ln(U_i)?
True or False:
ln(1 - U_i) can also be used in the above equation (M1L8). -
✔✔✔ Correct Answer > Exponential Distribution
, True - because (1 - U_i) is also uniform
True or false: output from simulations tend to be i.i.d. normally
distributed (M1L9). - ✔✔✔ Correct Answer > False! They tend
to be nasty and can't directly be analyzed with standard stats
tests.
Which type of simulation focuses on short-term behavior?
Examples include: Avg wait time in a bank for a day, avg # of
infected victims during a pandemic, and evaluating the
effectiveness of a marketing campaign over 3 months (M1L9). -
✔✔✔ Correct Answer > Terminating simulations
Which type of simulation focuses on long-term behavior?
Examples include: long-running assembly line in a factory,
performance of a transportation network under various
conditions, and an estimate of the unemployment rate 30 years
from now (M1L9). - ✔✔✔ Correct Answer > Steady-state
simulations
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