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ISYE 6644 FINAL EXAM 2024 NEWEST 2 VERSIONS (VERSION A AND B) COMPLETE ACCURATE EXAM QUESTIONS WITH DETAILED VERIFIED ANSWERS (100% CORRECT ANSWERS) /ALREADY GRADED A+$18.79
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ISYE 6644 FINAL EXAM 2024 NEWEST 2 VERSIONS (VERSION A AND B) COMPLETE ACCURATE EXAM QUESTIONS WITH DETAILED VERIFIED ANSWERS (100% CORRECT ANSWERS) /ALREADY GRADED A+
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Course
ISYE 6644
Institution
ISYE 6644
ISYE 6644 FINAL EXAM 2024 NEWEST 2 VERSIONS (VERSION A AND B) COMPLETE ACCURATE EXAM QUESTIONS WITH DETAILED VERIFIED ANSWERS (100% CORRECT ANSWERS) /ALREADY GRADED A+
ISYE 6644 FINAL EXAM 2024 NEWEST 2
VERSIONS (VERSION A AND B)
COMPLETE ACCURATE EXAM
QUESTIONS WITH DETAILED VERIFIED
ANSWERS (100% CORRECT ANSWERS)
/ALREADY GRADED A+
VERSION A
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
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