ISYE6644 EXAM WITH VERIFIED QUESTIONS
AND ANSWERS|| ALREADY GRADED A+ ||
GUARANTEED PASS || LATEST VERSION 2025
Suppose we're conducting a χ 2 goodness-of-fit test to determine whether or not
200 i.i.d. observations are from a Johnson distribution, which has 4 parameters
that must be estimated. If we divide the observations into 10 equal-probability
intervals, how many degrees of freedom will our test have? - ANSWER-10 − 4
− 1 = 5.
Which is the method of batch means more appropriate for: terminating or
steady-state simulations? - ANSWER-Steady-state
Which is usually a better way to deal with initialization bias in steady-state
simulation analysis: (i) make an extremely long run to overwhelm the bias, or
(ii) perform truncation? - ANSWER-Truncate
Consider the following 10 snowfall totals in Buffoonalo, NY over consecutive
years: 130 94 125 112 150 123 141 133 128 152 Use the method of batch means
to calculate a two - ANSWER-We use b = 2 batches here here. X¯ n = 128.8,
the batch means are X¯ 1,5 = 122.2 and X¯ 2,5 = 135.4, and the batch means
estimator for the variance parameter is VB = 435.6, the desired CI is [87.1,
170.5]
Suppose [0, 1] is a 90% confidence interval for the mean µ based on 10
independent replications of size 1000. Now the boss has decided that she wants
a 99% CI for 2µ based on those same 10 replications of size 1000. What is it? -
ANSWER-[-0.77, 2.77]
,Suppose I use the method of overlapping batch means with sample size n =
10000 and batch size m = 500. Approximately how many degrees of freedom
will the resulting variance estimator have? - ANSWER-Denote b = n/m = 20.
You get approximately 3/2(b − 1) = 28.5 d.f. (Will also accept 3b/2 = 30 or
anything reasonably close.)
If W(t) is a standard Brownian motion process and a < b, find Pr(W(a) < W(b)).
- ANSWER-W(a) − W(b) is normally distributed with mean 0. This
immediately yields a probability of 1/2.
Suppose that A = Integral0-1(B(t))dt is the area under a Brownian bridge
process. Find Pr(A > 1/ √ 12). - ANSWER-From class notes, we have A ∼
Nor(0, 1 12 ). Then Pr(A > 1/ √ 12) = Pr(Nor(0, 1) > 1) = 0.1587.
Suppose that I'm interested in selecting the most popular television show during
a particular time period. What kind of selection problem is this — (a) normal,
(b) multinomial, or (c) Bernoulli? - ANSWER-(b) multinomial
Suppose X and Y have joint p.d.f. f(x,y) = 8xy for all 0 < y < x < 1. Find
E[5X/4 -1/3] - ANSWER-2/3
YES or NO? Consider again the joint p.d.f. from the previous question, f(x,y) =
8xy for 0<y<x<1. Are X and Y dependent random variables? - ANSWER-Yes
Suppose U1 and U2 are i.i.d. Unif(0,1). What is the distribution of 5U1 - 5U2? -
ANSWER-Tria(-5,0,5)
Suppose U1 and U2 are i.i.d. Unif(0,1), and let X = sqrt(-2ln(U1))cos(2piU2).
Find PR(X<-1) - ANSWER-0.1587
If U1 and U2 are i.i.d. Unif(0,1), what is the distribution of -0.5ln[(1-
U1)^4U2^4]? - ANSWER-Erlang2(0.5)
, Suppose we are given a choice between two estimators, T1 and T2, and are told
that the relative efficiency of T1 to T2 is 0.8. That is, the Mean Square Error
(MSE) ratio between the two estimators is MSE(T2)/MSE(T1)= 1.8. Which
estimator would you choose and why? - ANSWER-Choose T1, it has a lower
MSE.
Consider a nonhomogeneous Poisson arrival process with rate function
lambda(t) = t/2 for t>= 0. Find the probability that there will be no more than
two arrivals before time t=2. - ANSWER-0.0803
Consider a 2x2 covariance matrix sigma = (3 2 2 5). Calculate the lower-
triangular matrix C such that CC' = sigma, and tell met e value of entry c21. -
ANSWER-2/sqrt(3)
Which one of the following properties of a Brownian motion process W(t) is
incorrect? - ANSWER-W(4)-W(2) has the same distribution as W(8)-W(4)
Let W(t) denote a Brownian motion process at time t. Let A = integral0-1W(t)dt
represent the area under the process from time t=0 to t=1. Find the probability
that A <=1. - ANSWER-0.9584
TRUE or FALSE? In ARENA, entities must be CREATE'd to get into te model,
and DISPOSE'd to leave. - ANSWER-True
TRUE or FALSE? In ARENA, queues cannot be defined manually; they can
only be (automatically) created by certain modules (e.g. PROCESS or SEIZE
modules). - ANSWER-False
TRUE or FALSE? The Komogorov-Smirnov test can be used both to see (i) if
data seem to fit to a particular hypothesized distribution, and (ii) if the data are
independent. - ANSWER-False
AND ANSWERS|| ALREADY GRADED A+ ||
GUARANTEED PASS || LATEST VERSION 2025
Suppose we're conducting a χ 2 goodness-of-fit test to determine whether or not
200 i.i.d. observations are from a Johnson distribution, which has 4 parameters
that must be estimated. If we divide the observations into 10 equal-probability
intervals, how many degrees of freedom will our test have? - ANSWER-10 − 4
− 1 = 5.
Which is the method of batch means more appropriate for: terminating or
steady-state simulations? - ANSWER-Steady-state
Which is usually a better way to deal with initialization bias in steady-state
simulation analysis: (i) make an extremely long run to overwhelm the bias, or
(ii) perform truncation? - ANSWER-Truncate
Consider the following 10 snowfall totals in Buffoonalo, NY over consecutive
years: 130 94 125 112 150 123 141 133 128 152 Use the method of batch means
to calculate a two - ANSWER-We use b = 2 batches here here. X¯ n = 128.8,
the batch means are X¯ 1,5 = 122.2 and X¯ 2,5 = 135.4, and the batch means
estimator for the variance parameter is VB = 435.6, the desired CI is [87.1,
170.5]
Suppose [0, 1] is a 90% confidence interval for the mean µ based on 10
independent replications of size 1000. Now the boss has decided that she wants
a 99% CI for 2µ based on those same 10 replications of size 1000. What is it? -
ANSWER-[-0.77, 2.77]
,Suppose I use the method of overlapping batch means with sample size n =
10000 and batch size m = 500. Approximately how many degrees of freedom
will the resulting variance estimator have? - ANSWER-Denote b = n/m = 20.
You get approximately 3/2(b − 1) = 28.5 d.f. (Will also accept 3b/2 = 30 or
anything reasonably close.)
If W(t) is a standard Brownian motion process and a < b, find Pr(W(a) < W(b)).
- ANSWER-W(a) − W(b) is normally distributed with mean 0. This
immediately yields a probability of 1/2.
Suppose that A = Integral0-1(B(t))dt is the area under a Brownian bridge
process. Find Pr(A > 1/ √ 12). - ANSWER-From class notes, we have A ∼
Nor(0, 1 12 ). Then Pr(A > 1/ √ 12) = Pr(Nor(0, 1) > 1) = 0.1587.
Suppose that I'm interested in selecting the most popular television show during
a particular time period. What kind of selection problem is this — (a) normal,
(b) multinomial, or (c) Bernoulli? - ANSWER-(b) multinomial
Suppose X and Y have joint p.d.f. f(x,y) = 8xy for all 0 < y < x < 1. Find
E[5X/4 -1/3] - ANSWER-2/3
YES or NO? Consider again the joint p.d.f. from the previous question, f(x,y) =
8xy for 0<y<x<1. Are X and Y dependent random variables? - ANSWER-Yes
Suppose U1 and U2 are i.i.d. Unif(0,1). What is the distribution of 5U1 - 5U2? -
ANSWER-Tria(-5,0,5)
Suppose U1 and U2 are i.i.d. Unif(0,1), and let X = sqrt(-2ln(U1))cos(2piU2).
Find PR(X<-1) - ANSWER-0.1587
If U1 and U2 are i.i.d. Unif(0,1), what is the distribution of -0.5ln[(1-
U1)^4U2^4]? - ANSWER-Erlang2(0.5)
, Suppose we are given a choice between two estimators, T1 and T2, and are told
that the relative efficiency of T1 to T2 is 0.8. That is, the Mean Square Error
(MSE) ratio between the two estimators is MSE(T2)/MSE(T1)= 1.8. Which
estimator would you choose and why? - ANSWER-Choose T1, it has a lower
MSE.
Consider a nonhomogeneous Poisson arrival process with rate function
lambda(t) = t/2 for t>= 0. Find the probability that there will be no more than
two arrivals before time t=2. - ANSWER-0.0803
Consider a 2x2 covariance matrix sigma = (3 2 2 5). Calculate the lower-
triangular matrix C such that CC' = sigma, and tell met e value of entry c21. -
ANSWER-2/sqrt(3)
Which one of the following properties of a Brownian motion process W(t) is
incorrect? - ANSWER-W(4)-W(2) has the same distribution as W(8)-W(4)
Let W(t) denote a Brownian motion process at time t. Let A = integral0-1W(t)dt
represent the area under the process from time t=0 to t=1. Find the probability
that A <=1. - ANSWER-0.9584
TRUE or FALSE? In ARENA, entities must be CREATE'd to get into te model,
and DISPOSE'd to leave. - ANSWER-True
TRUE or FALSE? In ARENA, queues cannot be defined manually; they can
only be (automatically) created by certain modules (e.g. PROCESS or SEIZE
modules). - ANSWER-False
TRUE or FALSE? The Komogorov-Smirnov test can be used both to see (i) if
data seem to fit to a particular hypothesized distribution, and (ii) if the data are
independent. - ANSWER-False
