ISYE 6644/ FINAL EXAM NEWEST
ACTUAL EXAM WITH COMPLETE
QUESTIONS AND DETAILED ANSWERS
LATEST UPDATE
Suppose that the MLE for a parameter θ is θ ^ = 4. Find the MLE for θ. - ✔✔✔
Correct Answer > Invariance immediately implies that the MLE of sqrt(θ) is
simply sqrt( θ ^) = 2θ ^ = 2
If you're in this course, then you should always love your. . . - ✔✔✔ Correct
Answer > Method of Moments !
TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d., then the MoM estimator for E [
X 3 ]is 1 n ∑ i = 1 n X i 3. - ✔✔✔ Correct Answer > TRUE (by definition of
MoM estimator)
Suppose H 0 is true, but you've just rejected it! What have you done? - ✔✔✔
Correct Answer > You've committed a Type I error.
Suppose that you are testing 100 observations to see if they are exponential (with
unknown rate parameter λ). You decide to break the hypothesized p.d.f. into 5
intervals. How many degrees of freedom will your resulting chi-square goodness-
offit test statistic have? - ✔✔✔ Correct Answer > The degrees of freedom is
k−1−s=5−1−1=3
TRUE or FALSE? The Weibull distribution is a special case of the exponential
distribution - ✔✔✔ Correct Answer > FALSE. (It's the other way around!)
,TRUE or FALSE? A search algorithm such as bisection or Newton is required to
obtain the MLEs for the two Weibull parameters. - ✔✔✔ Correct Answer > TRUE
(the r parameter of the Weibull distribution cannot be determined in closed form).
What does GIGO mean? - ✔✔✔ Correct Answer > Garbage-ingarbage-out
What's a good distribution for modeling heights of people? - ✔✔✔ Correct
Answer > Normal
What's a good distribution for modeling the number of random customer arrivals to
a store? - ✔✔✔ Correct Answer > The Poisson distribution is used for counting
the number of arrivals over some interval of time.
TRUE or FALSE? If the expected value of your estimator equals the parameter that
you're trying to estimate, then your estimator is unbiased. - ✔✔✔ Correct Answer
> TRUE. (This is the definition of unbiasedness in words.)
TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d. with mean μ, then the sample
mean X ¯ is unbiased for μ. - ✔✔✔ Correct Answer > TRUE
What is the MSE of an estimator? - ✔✔✔ Correct Answer >
𝐵𝑖𝑎𝑠^2+𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Suppose that X 1 = 4 , X 2 = 3 , X 3 = 5 are i.i.d. realizations from an E x p ( λ )
distribution. What is the MLE of λ? - ✔✔✔ Correct Answer > Since λ^ = 1/ X ¯ =
0.25
,TRUE or FALSE? It's possible to estimate two MLEs simultaneously, e.g., for the
N o r ( μ , σ 2 ) distribution. - ✔✔✔ Correct Answer > TRUE (it's possible based
on taking the partial derivatives of the likelihood function with respect to each
parameter).
TRUE or FALSE? Sometimes it might be difficult to obtain an MLE in closed
form. - ✔✔✔ Correct Answer > TRUE. (Think of the gamma example that we
did.)
goodness-of-fit tests - ✔✔✔ Correct Answer > KolmogorovSmirnov
Cramer-von Mises
Anderson-Darling
Shapiro-Wilk
Which of the following problematic issues can arise in input data analysis? - ✔✔✔
Correct Answer > Not enough data
Data coming from strange-looking, "non-standard" distributions
Nonstationary data (in which the distribution appears to change over time)
Correlated data
TRUE or FALSE? Arena has an Input Analyzer that automates distribution fitting
for certain well-known distributions. - ✔✔✔ Correct Answer > TRUE. (It's often a
great time-saver!
Suppose that a machine consists of components A, B, and C. If any of the
components fail, then the machine breaks down. The failure times for A, B, and C
are exponential (with probability 0.5), normal (w.p. 0.1), and Weibull (w.p. 0.4),
respectively.
, YES or NO? Would the composition method be a good choice to generate the
overall machine breakdown time for this scenario? - ✔✔✔ Correct Answer > YES.
Composition would be much more efficient than generating all three failure times
for A, B, and C, and then taking the minimum.
Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of ( H , W )? -
✔✔✔ Correct Answer > Bivariate normal distribution with positive correlation
coefficient
The multivariate normal distribution's covariance matrix ∑ can be decomposed into
the form ∑ = C C T. What does the C informally stand for? - ✔✔✔ Correct
Answer > Cholesky
TRUE or FALSE? The times between Poisson( λ ) arrivals are i.i.d. Exp( λ ). -
✔✔✔ Correct Answer > TRUE. (... as long as ( λ ) doesn't change over time.)
TRUE or FALSE? The times between nonhomogeneous Poisson( λ ) arrivals are
i.i.d. Exp( λ ). - ✔✔✔ Correct Answer > FALSE. (They're independent, but the
distribution changes as the arrival rate λ ( t ) changes over time.)
What is the recommended method to generate
nonhomogeneous Poisson arrivals? - ✔✔✔ Correct Answer > Thinning
Consider the time series Y i = ϕ Y i − 1 + ϵ i , i = 1 , 2 , ..., where the ϵ i's are i.i.d.
normal. What is this time series called? (Give the best answer.) - ✔✔✔ Correct
Answer > first-order autoregressive process
ACTUAL EXAM WITH COMPLETE
QUESTIONS AND DETAILED ANSWERS
LATEST UPDATE
Suppose that the MLE for a parameter θ is θ ^ = 4. Find the MLE for θ. - ✔✔✔
Correct Answer > Invariance immediately implies that the MLE of sqrt(θ) is
simply sqrt( θ ^) = 2θ ^ = 2
If you're in this course, then you should always love your. . . - ✔✔✔ Correct
Answer > Method of Moments !
TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d., then the MoM estimator for E [
X 3 ]is 1 n ∑ i = 1 n X i 3. - ✔✔✔ Correct Answer > TRUE (by definition of
MoM estimator)
Suppose H 0 is true, but you've just rejected it! What have you done? - ✔✔✔
Correct Answer > You've committed a Type I error.
Suppose that you are testing 100 observations to see if they are exponential (with
unknown rate parameter λ). You decide to break the hypothesized p.d.f. into 5
intervals. How many degrees of freedom will your resulting chi-square goodness-
offit test statistic have? - ✔✔✔ Correct Answer > The degrees of freedom is
k−1−s=5−1−1=3
TRUE or FALSE? The Weibull distribution is a special case of the exponential
distribution - ✔✔✔ Correct Answer > FALSE. (It's the other way around!)
,TRUE or FALSE? A search algorithm such as bisection or Newton is required to
obtain the MLEs for the two Weibull parameters. - ✔✔✔ Correct Answer > TRUE
(the r parameter of the Weibull distribution cannot be determined in closed form).
What does GIGO mean? - ✔✔✔ Correct Answer > Garbage-ingarbage-out
What's a good distribution for modeling heights of people? - ✔✔✔ Correct
Answer > Normal
What's a good distribution for modeling the number of random customer arrivals to
a store? - ✔✔✔ Correct Answer > The Poisson distribution is used for counting
the number of arrivals over some interval of time.
TRUE or FALSE? If the expected value of your estimator equals the parameter that
you're trying to estimate, then your estimator is unbiased. - ✔✔✔ Correct Answer
> TRUE. (This is the definition of unbiasedness in words.)
TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d. with mean μ, then the sample
mean X ¯ is unbiased for μ. - ✔✔✔ Correct Answer > TRUE
What is the MSE of an estimator? - ✔✔✔ Correct Answer >
𝐵𝑖𝑎𝑠^2+𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Suppose that X 1 = 4 , X 2 = 3 , X 3 = 5 are i.i.d. realizations from an E x p ( λ )
distribution. What is the MLE of λ? - ✔✔✔ Correct Answer > Since λ^ = 1/ X ¯ =
0.25
,TRUE or FALSE? It's possible to estimate two MLEs simultaneously, e.g., for the
N o r ( μ , σ 2 ) distribution. - ✔✔✔ Correct Answer > TRUE (it's possible based
on taking the partial derivatives of the likelihood function with respect to each
parameter).
TRUE or FALSE? Sometimes it might be difficult to obtain an MLE in closed
form. - ✔✔✔ Correct Answer > TRUE. (Think of the gamma example that we
did.)
goodness-of-fit tests - ✔✔✔ Correct Answer > KolmogorovSmirnov
Cramer-von Mises
Anderson-Darling
Shapiro-Wilk
Which of the following problematic issues can arise in input data analysis? - ✔✔✔
Correct Answer > Not enough data
Data coming from strange-looking, "non-standard" distributions
Nonstationary data (in which the distribution appears to change over time)
Correlated data
TRUE or FALSE? Arena has an Input Analyzer that automates distribution fitting
for certain well-known distributions. - ✔✔✔ Correct Answer > TRUE. (It's often a
great time-saver!
Suppose that a machine consists of components A, B, and C. If any of the
components fail, then the machine breaks down. The failure times for A, B, and C
are exponential (with probability 0.5), normal (w.p. 0.1), and Weibull (w.p. 0.4),
respectively.
, YES or NO? Would the composition method be a good choice to generate the
overall machine breakdown time for this scenario? - ✔✔✔ Correct Answer > YES.
Composition would be much more efficient than generating all three failure times
for A, B, and C, and then taking the minimum.
Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of ( H , W )? -
✔✔✔ Correct Answer > Bivariate normal distribution with positive correlation
coefficient
The multivariate normal distribution's covariance matrix ∑ can be decomposed into
the form ∑ = C C T. What does the C informally stand for? - ✔✔✔ Correct
Answer > Cholesky
TRUE or FALSE? The times between Poisson( λ ) arrivals are i.i.d. Exp( λ ). -
✔✔✔ Correct Answer > TRUE. (... as long as ( λ ) doesn't change over time.)
TRUE or FALSE? The times between nonhomogeneous Poisson( λ ) arrivals are
i.i.d. Exp( λ ). - ✔✔✔ Correct Answer > FALSE. (They're independent, but the
distribution changes as the arrival rate λ ( t ) changes over time.)
What is the recommended method to generate
nonhomogeneous Poisson arrivals? - ✔✔✔ Correct Answer > Thinning
Consider the time series Y i = ϕ Y i − 1 + ϵ i , i = 1 , 2 , ..., where the ϵ i's are i.i.d.
normal. What is this time series called? (Give the best answer.) - ✔✔✔ Correct
Answer > first-order autoregressive process
