ISYE 6644/ ISYE6644 FINAL EXAM NEWEST
ACTUAL EXAM WITH COMPLETE
QUESTIONS AND DETAILED ANSWERS
GRADED A | BRAND NEW!!!
What does GIGO mean? - ✔✔✔ Correct Answer > Garbage-in-
garbage-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.)
,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-of-
fit 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).
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
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