1|Page
ISYE 6644 FINAL EXAM VERSION 1 SIMULATION EXAM
NEWEST 2026/2027 COMPLETE QUESTIONS AND CORRECT
ANSWERS (VERIFIED ANSWERS) |ALREADY GRADED A+||JUST
OUT!!!
If X 1 , ... , X 10 are i.i.d. Pois(6), what is the expected value of
the sample variance S^2? - ANSWER-6
S^2 is always unbiased for the variance of X i. Thus, we have E [
S^2 ] = V a r ( X i ) = λ = 6
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-MSE = Bias^ 2
+ Var, so
M S E ( A ) = 9 + 12 = 21 and M S E ( B ) = 4 + 14 = 18.
If X 1 = 2, X 2 = − 2, and X 3 = 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-σ^2 = (n-
1)/n *S^2
8/3
Suppose we observe the Pois( λ ) realizationsX 1 = 5 , X 2 = 9
and X 3 = 1. What is the maximum likelihood estimate of λ? -
ANSWER-The likelihood function is
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L(λ)
Thus,
ln ( L ( λ ) )
This implies that
(d /d λ )*ln ( L ( λ ) ) = − n + (∑ i = 1 n x i )/ λ .
Setting the derivative to 0 and solving yields λ ^ = x ¯ = 5. Duh!
What a surprise!
Suppose that we have a number of observations from a Pois( λ )
distribution, and it turns out that the MLE for λ is λ ^ = 5.
What's the maximum likelihood estimate of Pr ( X = 3 )? -
ANSWER-By invariance,
Pr ^ ( X = k ) = e − λ ^ λ ^ k k ! ,
so that we have Pr ^ ( X = 3 ) = e − x ¯ x ¯ k k ! = e − 5 5 3 3 ! =
0.1404.
Suppose that we observe X 1 = 5, X 2 = 9, and X 3 = 1. What's
the method of moments estimate of E [ X 2 ]? - ANSWER-The
MOM estimator for E[X^2] = ( 25 + 81 + 1 ) / 3 =
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Consider the PRN's U 1 = 0.1 , U 2 = 0.9 , and U 3 = 0.2. Use
Kolmogorov-Smirnov with α = 0.05 to test to see if these
numbers are indeed uniform. Do we ACCEPT or REJECT
uniformity? - ANSWER-Accept
Since D < D α , n, we ACCEPT uniformity (though it's kind of a
joke since it's only based on 3 observations)
What does GIGO mean? - ANSWER-Garbage-in-garbage-out
What's a good distribution for modeling heights of people? -
ANSWER-Normal
What's a good distribution for modeling the number of random
customer arrivals to a store? - ANSWER-The Poisson distribution
is used for counting the number of arrivals over some interval
of time.
TRUE or FALSE? If the expected value of your estimator equals
the parameter that you're trying to estimate, then your
estimator is unbiased. - ANSWER-TRUE. (This is the definition of
unbiasedness in words.)
ISYE 6644 FINAL EXAM VERSION 1 SIMULATION EXAM
NEWEST 2026/2027 COMPLETE QUESTIONS AND CORRECT
ANSWERS (VERIFIED ANSWERS) |ALREADY GRADED A+||JUST
OUT!!!
If X 1 , ... , X 10 are i.i.d. Pois(6), what is the expected value of
the sample variance S^2? - ANSWER-6
S^2 is always unbiased for the variance of X i. Thus, we have E [
S^2 ] = V a r ( X i ) = λ = 6
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-MSE = Bias^ 2
+ Var, so
M S E ( A ) = 9 + 12 = 21 and M S E ( B ) = 4 + 14 = 18.
If X 1 = 2, X 2 = − 2, and X 3 = 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-σ^2 = (n-
1)/n *S^2
8/3
Suppose we observe the Pois( λ ) realizationsX 1 = 5 , X 2 = 9
and X 3 = 1. What is the maximum likelihood estimate of λ? -
ANSWER-The likelihood function is
,2|Page
L(λ)
Thus,
ln ( L ( λ ) )
This implies that
(d /d λ )*ln ( L ( λ ) ) = − n + (∑ i = 1 n x i )/ λ .
Setting the derivative to 0 and solving yields λ ^ = x ¯ = 5. Duh!
What a surprise!
Suppose that we have a number of observations from a Pois( λ )
distribution, and it turns out that the MLE for λ is λ ^ = 5.
What's the maximum likelihood estimate of Pr ( X = 3 )? -
ANSWER-By invariance,
Pr ^ ( X = k ) = e − λ ^ λ ^ k k ! ,
so that we have Pr ^ ( X = 3 ) = e − x ¯ x ¯ k k ! = e − 5 5 3 3 ! =
0.1404.
Suppose that we observe X 1 = 5, X 2 = 9, and X 3 = 1. What's
the method of moments estimate of E [ X 2 ]? - ANSWER-The
MOM estimator for E[X^2] = ( 25 + 81 + 1 ) / 3 =
, 3|Page
Consider the PRN's U 1 = 0.1 , U 2 = 0.9 , and U 3 = 0.2. Use
Kolmogorov-Smirnov with α = 0.05 to test to see if these
numbers are indeed uniform. Do we ACCEPT or REJECT
uniformity? - ANSWER-Accept
Since D < D α , n, we ACCEPT uniformity (though it's kind of a
joke since it's only based on 3 observations)
What does GIGO mean? - ANSWER-Garbage-in-garbage-out
What's a good distribution for modeling heights of people? -
ANSWER-Normal
What's a good distribution for modeling the number of random
customer arrivals to a store? - ANSWER-The Poisson distribution
is used for counting the number of arrivals over some interval
of time.
TRUE or FALSE? If the expected value of your estimator equals
the parameter that you're trying to estimate, then your
estimator is unbiased. - ANSWER-TRUE. (This is the definition of
unbiasedness in words.)
