ISYE 6644 SIMULATION EXAM |COMPLETE QUESTIONS WITH 100%
GRADED EXPERT SOLUTIONS | 100% CORRECT | GET A+
(8.3) Find the sample variance of -3, -2, -1, 0, 1, 2, 3 - (Answer)14/3 (or 4.666). If
sample is entire population than variance is 4.
(8.1) M/M/1 queue - (Answer)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 - (Answer)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 - (Answer)True.
(8.4) What is the MSE (Mean Squared Error) of an estimator? - (Answer)Bias^2 +
Variance
,(8.3) What is the expected value of the mean of a Pois(λ) random variable? -
(Answer)λ is the mean and the variance
(8.3) What is the expected sample variance s^2 of a Pois(λ) random variable? -
(Answer)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? - (Answer)B is lower. Bias^2 + Variance: 18 < 21
MLE - (Answer)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? - (Answer)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 likelihood estimate for the variance
σ^2? - (Answer)8/3. MLE of σ^2 is the summation of the squared differences (Xi -
μ), all divided by n.
(8.5/8.6) Suppose we observe the Pois(λ) realizations X1=5, X2=9 and X3=1.
What is the maximum likelihood estimate of λ? - (Answer)5. λ is estimated as the
summation of sample values divided by the number of sample values. (5+9+1)/3 =
5
(8.5) Suppose X1, ..., Xn are i.i.d. Bern(p). Find the MLE for p. - (Answer)
(8.7) Suppose that we have a number of observations from a Pois(λ) distribution,
and it turns out that the MLE for λ is λhat=5. What's the maximum likelihood
estimate of Pr(X=3)? - (Answer)0.1404. P(X=x) = λ^x * e^(−λ) / x!
(8.6) TRUE or FALSE? It's possible to estimate two MLEs simultaneously, e.g.,
for the Nor(μ,σ2) distribution. - (Answer)True
GRADED EXPERT SOLUTIONS | 100% CORRECT | GET A+
(8.3) Find the sample variance of -3, -2, -1, 0, 1, 2, 3 - (Answer)14/3 (or 4.666). If
sample is entire population than variance is 4.
(8.1) M/M/1 queue - (Answer)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 - (Answer)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 - (Answer)True.
(8.4) What is the MSE (Mean Squared Error) of an estimator? - (Answer)Bias^2 +
Variance
,(8.3) What is the expected value of the mean of a Pois(λ) random variable? -
(Answer)λ is the mean and the variance
(8.3) What is the expected sample variance s^2 of a Pois(λ) random variable? -
(Answer)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? - (Answer)B is lower. Bias^2 + Variance: 18 < 21
MLE - (Answer)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? - (Answer)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 likelihood estimate for the variance
σ^2? - (Answer)8/3. MLE of σ^2 is the summation of the squared differences (Xi -
μ), all divided by n.
(8.5/8.6) Suppose we observe the Pois(λ) realizations X1=5, X2=9 and X3=1.
What is the maximum likelihood estimate of λ? - (Answer)5. λ is estimated as the
summation of sample values divided by the number of sample values. (5+9+1)/3 =
5
(8.5) Suppose X1, ..., Xn are i.i.d. Bern(p). Find the MLE for p. - (Answer)
(8.7) Suppose that we have a number of observations from a Pois(λ) distribution,
and it turns out that the MLE for λ is λhat=5. What's the maximum likelihood
estimate of Pr(X=3)? - (Answer)0.1404. P(X=x) = λ^x * e^(−λ) / x!
(8.6) TRUE or FALSE? It's possible to estimate two MLEs simultaneously, e.g.,
for the Nor(μ,σ2) distribution. - (Answer)True
