ISYE-6644 Simulation 2025/2026 Exam
Questions and Answers | A+ Score
Assured
(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.
Questions and Answers | A+ Score
Assured
(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.
