ISYE-6644 Simulation UPDATED Actual Questions and CORRECT Answers
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Course
ISYE 6644
Institution
ISYE 6644
ISYE-6644 Simulation UPDATED Actual
Questions and CORRECT Answers
(8.3) Find the sample variance of -3, -2, -1, 0, 1, 2, 3 - CORRECT ANSWER- 14/3 (or
4.666). If sample is entire population than variance is 4.
(8.1) M/M/1 queue - CORRECT ANSWER- queue length having a single server.
(8.3) If t...
ISYE-6644 Simulation UPDATED Actual
Questions and CORRECT Answers
(8.3) Find the sample variance of -3, -2, -1, 0, 1, 2, 3 - CORRECT ANSWER✔✔- 14/3 (or
4.666). If sample is entire population than variance is 4.
(8.1) M/M/1 queue - CORRECT 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 - CORRECT 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 - CORRECT ANSWER✔✔- True.
(8.4) What is the MSE (Mean Squared Error) of an estimator? - CORRECT ANSWER✔✔-
Bias^2 + Variance
(8.3) What is the expected value of the mean of a Pois(λ) random variable? - CORRECT
ANSWER✔✔- λ is the mean and the variance
(8.3) What is the expected sample variance s^2 of a Pois(λ) random variable? - CORRECT
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? - CORRECT
ANSWER✔✔- B is lower. Bias^2 + Variance: 18 < 21
MLE - CORRECT 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? - CORRECT 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? - CORRECT
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? - CORRECT 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. - CORRECT 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)? -
CORRECT 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. - CORRECT ANSWER✔✔- True
(8.6) TRUE or FALSE? Sometimes it might be difficult to obtain an MLE in closed form. -
CORRECT ANSWER✔✔- True. (There is a gamma example.)
(8.7) Suppose that the MLE for a parameter θ is θhat=4. Find the MLE for √θ. - CORRECT
ANSWER✔✔- 2. Invariance immediately implies that the MLE of √θ is simply √θhat = 2
(8.8) Suppose that we observe X1 = 5, X2 = 9, and X3 = 1. What's the method of moments
estimate of E[X^2]? - CORRECT ANSWER✔✔- 35.6667. Second moment is the sum of the
squared samples divided by the number of samples. (5^2 + 9^2 + 1^2) / 3 = 35.666666667
(8.9) Suppose we're conducting a χ^2 goodness-of-fit test with Type I error rate α = 0.01 to
determine whether or not 100 i.i.d. observations are from a lognormal distribution with
unknown parameters μ and σ^2. If we divide the observations into 5 equal-probability
intervals and we observe a g-o-f statistic of χ0^2 = 11.2, will we ACCEPT (i.e., fail to reject)
or REJECT the null hypothesis of lognormality? - CORRECT ANSWER✔✔- Reject. k = 5,
subtract 1 and subtract 2 for the two unknown parameters (or had to estimate), so degrees of
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