ISYE 6644 Final Exam 2026 – A+ Simulation Solutions & Full Review | Georgia Tech

10/3/21, 3:55 PM ISYyE 6644 - Summer 2021 - Final Exam : Simulation - ISYE-6644-A/OAN/O01


Attempt History
Attempt Time Score

LATEST Attempt1 120 minutes 73 out of 100




Score for this quiz: 73 out of 100
Submitted Aug 5 at 6:13pm
This attempt took 120 minutes.
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Question 1 3/3pts |


Suppose X and Y have joint p.df. f(z,y) =8zyforall0 <y<z < 1.
Find B [3X — 1].



Correct! b 2/3




Question 2


YES or NO? Consider again the joint p.d.f. from the previous question,
flz,y) =8zyfor0 <y <z <1
Are X and Y dependent random variables?


Correct! a. Yes


b. No


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,10/3/21, 3:55 PM ISYyE 6644 - Summer 2021 - Final Exam : Simulation - ISYE-6644-A/OAN/O01




. B
Question 3 3/3pts |

If X and Y are i.i.d. Nor(1, 2) random variables, find Var(X — Y + 2).




b. 0.5


c. 1


d.2


Correct! e 4




0/3pts |
|



Question 4
’7




If Z1,Z3, -+ -, Zay, areiid. Nor(0,1), whatis the distribution of
2n 2
1=1 Zi ?




a. Nor(0, 2n)


b. Pois(2n)

orrect Answer c. x2(2n)

ou Answered d. Both (b) and (c)



e. All of the above.




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, 10/3/21, 3:55 PM ISYyE 6644 - Summer 2021 - Final Exam : Simulation - ISYE-6644-A/OAN/O01

[ ]
Question 5 3/3pts |


Suppose Uy and U are i.i.d. Unif(0, 1). What is the distribution of
5U; — bUy ?



a. Unif(—5, 5)


b. Unif(0, 10)


c. Tria(—10, 0, 10)

Correct!
d. Tria(—5, 0, 5)

e. Tria(0, 5, 10)




Question 6 3/3pts |


Suppose U; and U; are i.i.d. Unif(0, 1), and let
X = /—2In(U,;) cos(2xU,). Find Pr(X < —1).


a.0


Correct! b 0.1587



c. 0.50


d. 0.8413


e. 1.00




{ R
- Question 7 3/3pts |
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