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