ISYE-6644 Simulation Questions and Answers with Verified Solutions |
Latest 2026 Update
Q: (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.
Q: (8.1) M/M/1 queue
Answer:
queue length having a single server.
Q: (8.3) If the expected value of your estimator equals the parameter that you're
trying to
Answer:
estimate, then your estimator is unbiased. True of False True. This is the definition of
unbiasedness
,ISYE-6644 Simulation Questions and Answers with Verified Solutions |
Latest 2026 Update
Q: (8.3) If X1, X2, ..., Xn are i.i.d. with mean mu, then the sample mean X-bar is
unbiased for mu.
Answer:
True or False True.
Q: (8.4) What is the MSE (Mean Squared Error) of an estimator?
Answer:
Bias^2 + Variance
Q: (8.3) What is the expected value of the mean of a Pois(λ) random variable?
Answer:
λ is the mean and the variance
Q: (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
, ISYE-6644 Simulation Questions and Answers with Verified Solutions |
Latest 2026 Update
Q: (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
Q: 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."
Q: (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
Latest 2026 Update
Q: (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.
Q: (8.1) M/M/1 queue
Answer:
queue length having a single server.
Q: (8.3) If the expected value of your estimator equals the parameter that you're
trying to
Answer:
estimate, then your estimator is unbiased. True of False True. This is the definition of
unbiasedness
,ISYE-6644 Simulation Questions and Answers with Verified Solutions |
Latest 2026 Update
Q: (8.3) If X1, X2, ..., Xn are i.i.d. with mean mu, then the sample mean X-bar is
unbiased for mu.
Answer:
True or False True.
Q: (8.4) What is the MSE (Mean Squared Error) of an estimator?
Answer:
Bias^2 + Variance
Q: (8.3) What is the expected value of the mean of a Pois(λ) random variable?
Answer:
λ is the mean and the variance
Q: (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
, ISYE-6644 Simulation Questions and Answers with Verified Solutions |
Latest 2026 Update
Q: (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
Q: 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."
Q: (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
