ISYE 6644 Midterm and Final Exam Questions &
Answers
Which property is not desirable for a good pseudo-random number
generator?
(Ans- We must be able to look up the series of PRNs from a table.
Which of the following PRN generators aren't very good?
(Ans- 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?
(Ans- True. (1XOR1)XOR1 = 0XOR1 = 1
TRUE or FALSE? There are good PRN generators out there having
incredible cycle lengths of over 2^100
(Ans- True
TRUE or FALSE? RANDU is a pretty good generator.
(Ans- 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?
(Ans- True
In the context of evaluating a PRN generator, which kinds of statistical
tests are we interested in?
(Ans- 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?
(Ans- 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.
(Ans- True
YES or NO? Does Xi = (Xi-1 + 12)mod(13) have full period?
(Ans- Yes, it trivially cycles through 0,1,2,....,11
, Which uniform generator was recommended in class, at least as a
desert island generator?
(Ans- 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
(Ans- True
Which of the following statements about the RANDU generator is true?
(Ans- 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?
(Ans- 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.
(Ans- True
Answers
Which property is not desirable for a good pseudo-random number
generator?
(Ans- We must be able to look up the series of PRNs from a table.
Which of the following PRN generators aren't very good?
(Ans- 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?
(Ans- True. (1XOR1)XOR1 = 0XOR1 = 1
TRUE or FALSE? There are good PRN generators out there having
incredible cycle lengths of over 2^100
(Ans- True
TRUE or FALSE? RANDU is a pretty good generator.
(Ans- 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?
(Ans- True
In the context of evaluating a PRN generator, which kinds of statistical
tests are we interested in?
(Ans- 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?
(Ans- 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.
(Ans- True
YES or NO? Does Xi = (Xi-1 + 12)mod(13) have full period?
(Ans- Yes, it trivially cycles through 0,1,2,....,11
, Which uniform generator was recommended in class, at least as a
desert island generator?
(Ans- 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
(Ans- True
Which of the following statements about the RANDU generator is true?
(Ans- 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?
(Ans- 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.
(Ans- True
