1|Page
ISYE6644 MIDTERM 2 NEWEST 2025 ACTUAL
EXAM COMPLETE ALL 130 QUESTIONS AND
CORRECT DETAILED ANSWERS (VERIFIED
ANSWERS) |ALREADY GRADED A+ (BRAND
NEW VERSION!!)
Which property is not desirable for a good pseudo-random
number generator? - ANSWER-We must be able to look up the
series of PRNs from a table.
Which of the following PRN generators aren't very good? -
ANSWER-Generators involving physical devices such as coin
flips or at least significant digit readings from an atomic clock,
random number tables, von Neuman's mid-square method,
Fibonacci and additive congruential generators.
TRUE or FALSE? (1XOR1)XOR1 = 1? - ANSWER-True.
(1XOR1)XOR1 = 0XOR1 = 1
TRUE or FALSE? There are good PRN generators out there
having incredible cycle lengths of over 2^100 - ANSWER-True
,2|Page
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
, 3|Page
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
ISYE6644 MIDTERM 2 NEWEST 2025 ACTUAL
EXAM COMPLETE ALL 130 QUESTIONS AND
CORRECT DETAILED ANSWERS (VERIFIED
ANSWERS) |ALREADY GRADED A+ (BRAND
NEW VERSION!!)
Which property is not desirable for a good pseudo-random
number generator? - ANSWER-We must be able to look up the
series of PRNs from a table.
Which of the following PRN generators aren't very good? -
ANSWER-Generators involving physical devices such as coin
flips or at least significant digit readings from an atomic clock,
random number tables, von Neuman's mid-square method,
Fibonacci and additive congruential generators.
TRUE or FALSE? (1XOR1)XOR1 = 1? - ANSWER-True.
(1XOR1)XOR1 = 0XOR1 = 1
TRUE or FALSE? There are good PRN generators out there
having incredible cycle lengths of over 2^100 - ANSWER-True
,2|Page
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
, 3|Page
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
