ISYE 6644/ ISYE6644 FINAL EXAM NEWEST
m m m m m
ACTUAL EXAM WITH COMPLETE QUES m m m m
TIONS AND DETAILED ANSWERS GRA m m m m
DED A | BRAND NEW!!! m m m m
What does GIGO mean? - ✔✔✔ Correct Answer > Garbage-in-
m m m m m m m m m
garbage-out
m
What's a good distribution for modeling heights of people? -
m m m m m m m m m
✔✔✔ Correct Answer > Normal
m m m m
What's a good distribution for modeling the number of random cu
m m m m m m m m m m
stomer arrivals to a store? -
m m m m m
m✔✔✔ Correct Answer > The Poisson distribution is used for coun
m m m m m m m m m m
ting the number of arrivals over some interval of time.
m m m m m m m m m
TRUE or FALSE? If the expected value of your estimator equals t
m m m m m m m m m m m
he parameter that you're trying to estimate, then your estimato
m m m m m m m m m
r is unbiased. -
m m m
m✔✔✔ Correct Answer > TRUE. (This is the definition of unbiase
m m m m m m m m m m
dness in words.)m m
,TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d. with mean μ, then
m m m m m m m m m m m m m m m m m m m m m
the sample mean X ¯ is unbiased for μ. - ✔✔✔ Correct Answer
m m m m m m m m m m m m
> TRUE
m
What is the MSE of an estimator? - ✔✔✔ Correct Answer >
m m m m m m m m m m m
𝐵𝑖𝑎𝑠^2+𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Suppose that X 1 = 4 , X 2 = 3 , X 3 = 5 are i.i.d. realizations from
m m m m m m m m m m m m m m m m m m m
man E x p ( λ ) distribution. What is the MLE of λ? -
m m m m m m m m m m m m m m
m✔✔✔ Correct Answer > Since λ^ = 1/ X ¯ = 0.25
m m m m m m m m m m m
TRUE or FALSE? It's possible to estimate two MLEs simultaneou
m m m m m m m m m
sly, e.g., for the N o r ( μ , σ 2 ) distribution. -
m m m m m m m m m m m m m m
m✔✔✔ Correct Answer > TRUE (it's possible based on taking the
m m m m m m m m m m
mpartial derivatives of the likelihood function with respect to eac
m m m m m m m m m
h parameter).
m
TRUE or FALSE? Sometimes it might be difficult to obtain an ML
m m m m m m m m m m m
E in closed form. -
m m m m
m✔✔✔ Correct Answer > TRUE. (Think of the gamma example th
m m m m m m m m m m
at we did.)
m m
,Suppose that the MLE for a parameter θ is θ ^ = 4. Find the MLE
m m m m m m m m m m m m m m m m
for θ. - m m
m✔✔✔ Correct Answer > Invariance immediately implies that th
m m m m m m m m
e MLE of sqrt(θ) is simply sqrt( θ ^) = 2θ ^ = 2
m m m m m m m m m m m m m
If you're in this course, then you should always love your. . . -
m m m m m m m m m m m m m
✔✔✔ Correct Answer > Method of Moments !
m m m m m m m
TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d., then the MoM es
m m m m m m m m m m m m m m m m m m m m m
timator for E [ X 3 ]is 1 n ∑ i = 1 n X i 3. -
m m m m m m m m m m m m m m m m m
m✔✔✔ Correct Answer > TRUE (by definition of MoM estimat
m m m m m m m m m
or)
Suppose H 0 is true, but you've just rejected it! What have you d
m m m m m m m m m m m m m
one? - m
m✔✔✔ Correct Answer > You've committed a Type I error.
m m m m m m m m m
Suppose that you are testing 100 observations to see if they are
m m m m m m m m m m m
mexponential (with unknown rate parameter λ). You decide to br
m m m m m m m m m
eak the hypothesized p.d.f. into 5 intervals. How many degrees
m m m m m m m m m m
of freedom will your resulting chi-square goodness-of-
m m m m m m
mfit test statistic have? -
m m m m
m✔✔✔ Correct Answer > The degrees of freedom is k−1−s=5−1−
m m m m m m m m m
1=3
, TRUE or FALSE? The Weibull distribution is a special case of the
m m m m m m m m m m m m
exponential distribution - m m
m✔✔✔ Correct Answer > FALSE. (It's the other way around!)
m m m m m m m m m
TRUE or FALSE? A search algorithm such as bisection or Newton
m m m m m m m m m m m
is required to obtain the MLEs for the two Weibull parameters.
m m m m m m m m m m
-
m✔✔✔ Correct Answer > TRUE (the r parameter of the Weibull d
m m m m m m m m m m m
istribution cannot be determined in closed form).
m m m m m m
goodness-of-fit tests - ✔✔✔ Correct Answer > Kolmogorov- m m m m m m m
mSmirnov
Cramer-
von Mises Anders
m m
on-
Darling Shapiro- m
Wilk
Which of the following problematic issues can arise in input da
m m m m m m m m m m
ta analysis? - ✔✔✔ Correct Answer > Not enough data
m m m m m m m m m
Data coming from strange-looking, "non-standard" distributions
m m m m m
Nonstationary data (in which the distribution appears to chan
m m m m m m m m
ge over time)
m m
Correlated data m
m m m m m
ACTUAL EXAM WITH COMPLETE QUES m m m m
TIONS AND DETAILED ANSWERS GRA m m m m
DED A | BRAND NEW!!! m m m m
What does GIGO mean? - ✔✔✔ Correct Answer > Garbage-in-
m m m m m m m m m
garbage-out
m
What's a good distribution for modeling heights of people? -
m m m m m m m m m
✔✔✔ Correct Answer > Normal
m m m m
What's a good distribution for modeling the number of random cu
m m m m m m m m m m
stomer arrivals to a store? -
m m m m m
m✔✔✔ Correct Answer > The Poisson distribution is used for coun
m m m m m m m m m m
ting the number of arrivals over some interval of time.
m m m m m m m m m
TRUE or FALSE? If the expected value of your estimator equals t
m m m m m m m m m m m
he parameter that you're trying to estimate, then your estimato
m m m m m m m m m
r is unbiased. -
m m m
m✔✔✔ Correct Answer > TRUE. (This is the definition of unbiase
m m m m m m m m m m
dness in words.)m m
,TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d. with mean μ, then
m m m m m m m m m m m m m m m m m m m m m
the sample mean X ¯ is unbiased for μ. - ✔✔✔ Correct Answer
m m m m m m m m m m m m
> TRUE
m
What is the MSE of an estimator? - ✔✔✔ Correct Answer >
m m m m m m m m m m m
𝐵𝑖𝑎𝑠^2+𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Suppose that X 1 = 4 , X 2 = 3 , X 3 = 5 are i.i.d. realizations from
m m m m m m m m m m m m m m m m m m m
man E x p ( λ ) distribution. What is the MLE of λ? -
m m m m m m m m m m m m m m
m✔✔✔ Correct Answer > Since λ^ = 1/ X ¯ = 0.25
m m m m m m m m m m m
TRUE or FALSE? It's possible to estimate two MLEs simultaneou
m m m m m m m m m
sly, e.g., for the N o r ( μ , σ 2 ) distribution. -
m m m m m m m m m m m m m m
m✔✔✔ Correct Answer > TRUE (it's possible based on taking the
m m m m m m m m m m
mpartial derivatives of the likelihood function with respect to eac
m m m m m m m m m
h parameter).
m
TRUE or FALSE? Sometimes it might be difficult to obtain an ML
m m m m m m m m m m m
E in closed form. -
m m m m
m✔✔✔ Correct Answer > TRUE. (Think of the gamma example th
m m m m m m m m m m
at we did.)
m m
,Suppose that the MLE for a parameter θ is θ ^ = 4. Find the MLE
m m m m m m m m m m m m m m m m
for θ. - m m
m✔✔✔ Correct Answer > Invariance immediately implies that th
m m m m m m m m
e MLE of sqrt(θ) is simply sqrt( θ ^) = 2θ ^ = 2
m m m m m m m m m m m m m
If you're in this course, then you should always love your. . . -
m m m m m m m m m m m m m
✔✔✔ Correct Answer > Method of Moments !
m m m m m m m
TRUE or FALSE? If X 1 , X 2 , . . . , X n are i.i.d., then the MoM es
m m m m m m m m m m m m m m m m m m m m m
timator for E [ X 3 ]is 1 n ∑ i = 1 n X i 3. -
m m m m m m m m m m m m m m m m m
m✔✔✔ Correct Answer > TRUE (by definition of MoM estimat
m m m m m m m m m
or)
Suppose H 0 is true, but you've just rejected it! What have you d
m m m m m m m m m m m m m
one? - m
m✔✔✔ Correct Answer > You've committed a Type I error.
m m m m m m m m m
Suppose that you are testing 100 observations to see if they are
m m m m m m m m m m m
mexponential (with unknown rate parameter λ). You decide to br
m m m m m m m m m
eak the hypothesized p.d.f. into 5 intervals. How many degrees
m m m m m m m m m m
of freedom will your resulting chi-square goodness-of-
m m m m m m
mfit test statistic have? -
m m m m
m✔✔✔ Correct Answer > The degrees of freedom is k−1−s=5−1−
m m m m m m m m m
1=3
, TRUE or FALSE? The Weibull distribution is a special case of the
m m m m m m m m m m m m
exponential distribution - m m
m✔✔✔ Correct Answer > FALSE. (It's the other way around!)
m m m m m m m m m
TRUE or FALSE? A search algorithm such as bisection or Newton
m m m m m m m m m m m
is required to obtain the MLEs for the two Weibull parameters.
m m m m m m m m m m
-
m✔✔✔ Correct Answer > TRUE (the r parameter of the Weibull d
m m m m m m m m m m m
istribution cannot be determined in closed form).
m m m m m m
goodness-of-fit tests - ✔✔✔ Correct Answer > Kolmogorov- m m m m m m m
mSmirnov
Cramer-
von Mises Anders
m m
on-
Darling Shapiro- m
Wilk
Which of the following problematic issues can arise in input da
m m m m m m m m m m
ta analysis? - ✔✔✔ Correct Answer > Not enough data
m m m m m m m m m
Data coming from strange-looking, "non-standard" distributions
m m m m m
Nonstationary data (in which the distribution appears to chan
m m m m m m m m
ge over time)
m m
Correlated data m
