ISYE-6644 Simulation UPDATED Actual Questions and CORRECT Answers
3 views 0 purchase
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller MGRADES. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.49. You're not tied to anything after your purchase.
