ISYE 6644 STUDY GUIDE EXAMS SET TEST
PAPER QUESTIONS AND SOLUTIONS 2026
VIEW AHEAD EXAM.
◍ TRUE or FALSE? There are good PRN generators out there having
incredible cycle lengths of over 2^100 Answer: True
◍ TRUE or FALSE? RANDU is a pretty good generator. Answer:
False. RANDU has several problems with hyperplanes.
◍ TRUE or FALSE? Alpha =P(Reject Ho|Ho is true) is the
probability of a Type 1 error? 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
◍ If the chi-squared goodness-of-fit statistic is much greater than the
relevant quantile, what do we do? 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. Answer: True
◍ YES or NO? Does Xi = (Xi-1 + 12)mod(13) have full period?
Answer: Yes, it trivially cycles through 0,1,2,....,11
, ◍ Which uniform generator was recommended in class, at least as a
desert island generator? 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 Answer:
True
◍ Which of the following statements about the RANDU generator is
true? 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?
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. Answer: True
◍ If X is a continuous variable with c.d.f. F(x), what's the distribution
of F(X)? Answer: Unif(0,1). Inverse transform theorem.
PAPER QUESTIONS AND SOLUTIONS 2026
VIEW AHEAD EXAM.
◍ TRUE or FALSE? There are good PRN generators out there having
incredible cycle lengths of over 2^100 Answer: True
◍ TRUE or FALSE? RANDU is a pretty good generator. Answer:
False. RANDU has several problems with hyperplanes.
◍ TRUE or FALSE? Alpha =P(Reject Ho|Ho is true) is the
probability of a Type 1 error? 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
◍ If the chi-squared goodness-of-fit statistic is much greater than the
relevant quantile, what do we do? 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. Answer: True
◍ YES or NO? Does Xi = (Xi-1 + 12)mod(13) have full period?
Answer: Yes, it trivially cycles through 0,1,2,....,11
, ◍ Which uniform generator was recommended in class, at least as a
desert island generator? 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 Answer:
True
◍ Which of the following statements about the RANDU generator is
true? 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?
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. Answer: True
◍ If X is a continuous variable with c.d.f. F(x), what's the distribution
of F(X)? Answer: Unif(0,1). Inverse transform theorem.
