ISYE-6644 Simulation EXAM QUESTIONS |\ |\ |\ |\
WITH ANSWERS |\
(8.3) Find the sample variance of -3, -2, -1, 0, 1, 2, 3 - CORRECT
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ANSWERS ✔✔14/3 (or 4.666). If sample is entire population than
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variance is 4. |\ |\
(8.1) M/M/1 queue - CORRECT ANSWERS ✔✔queue length having
|\ |\ |\ |\ |\ |\ |\ |\
a single server.
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(8.3) If the expected value of your estimator equals the parameter
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
that you're trying to estimate, then your estimator is unbiased. True
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
of False - CORRECT ANSWERS ✔✔True. This is the definition of
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unbiasedness
(8.3) If X1, X2, ..., Xn are i.i.d. with mean mu, then the sample
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
mean X-bar is unbiased for mu. True or False - CORRECT
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ANSWERS ✔✔True. |\
(8.4) What is the MSE (Mean Squared Error) of an estimator? -
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
CORRECT ANSWERS ✔✔Bias^2 + Variance |\ |\ |\ |\
, (8.3) What is the expected value of the mean of a Pois(λ) random
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
variable? - CORRECT ANSWERS ✔✔λ is the mean and the
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variance
(8.3) What is the expected sample variance s^2 of a Pois(λ) random
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
variable? - CORRECT ANSWERS ✔✔λ is the sample variance and
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the mean |\
(8.4) Suppose that estimator A has bias = 3 and variance = 12,
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while estimator B has bias -2 and variance = 14. Which estimator
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
(A or B) has the lower mean squared error? - CORRECT ANSWERS
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✔✔B is lower. Bias^2 + Variance: 18 < 21
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MLE - CORRECT ANSWERS ✔✔Maximum Likelihood Estimator -
|\ |\ |\ |\ |\ |\ |\
"A method of estimating the parameters of a distribution by
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
maximizing a likelihood function, so that under the assumed |\ |\ |\ |\ |\ |\ |\ |\ |\
statistical model the observed data is most probable."
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(8.4) Suppose that X1=4, X2=3, X3=5 are i.i.d. realizations from an
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Exp(λ) distribution. What is the MLE of λ? - CORRECT ANSWERS
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✔✔0.25
(8.5/8.6) If X1=2, X2=−2, and X3=0 are i.i.d. realizations from a
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Nor(μ , σ^2) distribution, what is the value of the maximum
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WITH ANSWERS |\
(8.3) Find the sample variance of -3, -2, -1, 0, 1, 2, 3 - CORRECT
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
ANSWERS ✔✔14/3 (or 4.666). If sample is entire population than
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
variance is 4. |\ |\
(8.1) M/M/1 queue - CORRECT ANSWERS ✔✔queue length having
|\ |\ |\ |\ |\ |\ |\ |\
a single server.
|\ |\ |\
(8.3) If the expected value of your estimator equals the parameter
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
that you're trying to estimate, then your estimator is unbiased. True
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
of False - CORRECT ANSWERS ✔✔True. This is the definition of
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
unbiasedness
(8.3) If X1, X2, ..., Xn are i.i.d. with mean mu, then the sample
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
mean X-bar is unbiased for mu. True or False - CORRECT
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
ANSWERS ✔✔True. |\
(8.4) What is the MSE (Mean Squared Error) of an estimator? -
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
CORRECT ANSWERS ✔✔Bias^2 + Variance |\ |\ |\ |\
, (8.3) What is the expected value of the mean of a Pois(λ) random
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
variable? - CORRECT ANSWERS ✔✔λ is the mean and the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
variance
(8.3) What is the expected sample variance s^2 of a Pois(λ) random
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
variable? - CORRECT ANSWERS ✔✔λ is the sample variance and
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
the mean |\
(8.4) Suppose that estimator A has bias = 3 and variance = 12,
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
while estimator B has bias -2 and variance = 14. Which estimator
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
(A or B) has the lower mean squared error? - CORRECT ANSWERS
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
✔✔B is lower. Bias^2 + Variance: 18 < 21
|\ |\ |\ |\ |\ |\ |\ |\ |\
MLE - CORRECT ANSWERS ✔✔Maximum Likelihood Estimator -
|\ |\ |\ |\ |\ |\ |\
"A method of estimating the parameters of a distribution by
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
maximizing a likelihood function, so that under the assumed |\ |\ |\ |\ |\ |\ |\ |\ |\
statistical model the observed data is most probable."
|\ |\ |\ |\ |\ |\ |\
(8.4) Suppose that X1=4, X2=3, X3=5 are i.i.d. realizations from an
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
Exp(λ) distribution. What is the MLE of λ? - CORRECT ANSWERS
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
✔✔0.25
(8.5/8.6) If X1=2, X2=−2, and X3=0 are i.i.d. realizations from a
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
Nor(μ , σ^2) distribution, what is the value of the maximum
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
