ISYE 6644 EXAM ACTUAL EXAM 2026 | ALL QUESTIONS AND CORRECT ANSWERS
| VERIFIED ANSWERS | SIMULATION AND MODELING FOR ENGINEERING AND
SCIENCE | GEORGIA INSTITUTE OF TECHNOLOGY
In the context of evaluating a PRN generator, which kinds of statistical
tests are we interested in? ------------Correct Answer--------------------
Goodness-of-fit tests, independence tests
If the chi-squared goodness-of-fit statistic is much greater than the
relevant quantile, what do we do? ------------Correct Answer----------------
----Reject the goodness-of-fit test and declare that the PRNs are
probably not uniform.
TRUE or FALSE? It's actually a good thing for you to be able to
reproduce a sequence of PRNs, should you so desire. ------------Correct
Answer--------------------True
YES or NO? Does Xi = (Xi-1 + 12)mod(13) have full period? ------------
Correct Answer--------------------Yes, it trivially cycles through 0,1,2,....,11
,Which uniform generator was recommended in class, at least as a
desert island generator? ------------Correct Answer--------------------Xi =
16807mod(2^31 - 1)
TRUE or FALSE? There are some great PRN generators out there with
incredible cycle lengths ~ 2^191 and even 2^19937 ------------Correct
Answer--------------------True
Which of the following statements about the RANDU generator is true?
------------Correct Answer--------------------Something just ain't right about
that boy, the generator is given by Xi = 65539Xi-1mod(2^31), the PRNs
appear at first glance to be uniform, but funny things happen when you
look at the plots of the PRNs in multiple dimensions, the PRNs are
distributed on just 15 hyperplanes.
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? ------------Correct
Answer--------------------Type II - You have incorrectly accepted the null
hypothesis of innocence.
, TRUE or FALSE? Unif(0,1) pseudo-random numbers can be used to
generate pretty much any other random variates, e.g. exponential,
normal, and Poisson. ------------Correct Answer--------------------True
If X is a continuous variable with c.d.f. F(x), what's the distribution of
F(X)? ------------Correct Answer--------------------Unif(0,1). Inverse
transform theorem.
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for
0<x<1. Why is acceptance-rejection a good method to use to generate
X? ------------Correct Answer--------------------Because the c.d.f. of X is very
hard to invert.
Unif(0,1) PRNs can be used to generate which of the following random
entities? ------------Correct Answer--------------------Exp(lambda) random
variates, Nor(0,1) random variates, Triangular random variates, Bern(p)
random variates, Nonhomogeneous Poisson processes, and just about
anything else.
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)? ----------
--Correct Answer--------------------Unif(0,1). Inverse transform theroem.
| VERIFIED ANSWERS | SIMULATION AND MODELING FOR ENGINEERING AND
SCIENCE | GEORGIA INSTITUTE OF TECHNOLOGY
In the context of evaluating a PRN generator, which kinds of statistical
tests are we interested in? ------------Correct Answer--------------------
Goodness-of-fit tests, independence tests
If the chi-squared goodness-of-fit statistic is much greater than the
relevant quantile, what do we do? ------------Correct Answer----------------
----Reject the goodness-of-fit test and declare that the PRNs are
probably not uniform.
TRUE or FALSE? It's actually a good thing for you to be able to
reproduce a sequence of PRNs, should you so desire. ------------Correct
Answer--------------------True
YES or NO? Does Xi = (Xi-1 + 12)mod(13) have full period? ------------
Correct Answer--------------------Yes, it trivially cycles through 0,1,2,....,11
,Which uniform generator was recommended in class, at least as a
desert island generator? ------------Correct Answer--------------------Xi =
16807mod(2^31 - 1)
TRUE or FALSE? There are some great PRN generators out there with
incredible cycle lengths ~ 2^191 and even 2^19937 ------------Correct
Answer--------------------True
Which of the following statements about the RANDU generator is true?
------------Correct Answer--------------------Something just ain't right about
that boy, the generator is given by Xi = 65539Xi-1mod(2^31), the PRNs
appear at first glance to be uniform, but funny things happen when you
look at the plots of the PRNs in multiple dimensions, the PRNs are
distributed on just 15 hyperplanes.
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? ------------Correct
Answer--------------------Type II - You have incorrectly accepted the null
hypothesis of innocence.
, TRUE or FALSE? Unif(0,1) pseudo-random numbers can be used to
generate pretty much any other random variates, e.g. exponential,
normal, and Poisson. ------------Correct Answer--------------------True
If X is a continuous variable with c.d.f. F(x), what's the distribution of
F(X)? ------------Correct Answer--------------------Unif(0,1). Inverse
transform theorem.
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for
0<x<1. Why is acceptance-rejection a good method to use to generate
X? ------------Correct Answer--------------------Because the c.d.f. of X is very
hard to invert.
Unif(0,1) PRNs can be used to generate which of the following random
entities? ------------Correct Answer--------------------Exp(lambda) random
variates, Nor(0,1) random variates, Triangular random variates, Bern(p)
random variates, Nonhomogeneous Poisson processes, and just about
anything else.
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)? ----------
--Correct Answer--------------------Unif(0,1). Inverse transform theroem.
