ISyE 6644 Summer 2021 Final Exam Simulation Solutions & Practice

ISyE 6644 - Summer 2021 - Final Exam
Attempt History
n,




Attempt Time Score
LATEST Attempt n,1 120 n,minutes 73 n,out n,of n,100



Score n,for n,this n,quiz: n,73 n,out n,of n,100
Submitted n,Aug n,5 n,at n,6:13pm
n,


This n,attempt n,took n,120 n,minutes.


Question 1 pts


Suppose X and Y have joint p.d.f. f(x, y) = 8xy for all 0 < y < x < 1.
Find E [ 5 − 1 ].
X
4 3


a. 1/5


Correct! b. 2/3


c. 4/5


d. 5/6


e. 1




Question 2 pts


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?


Correct! a. Yes

1/19
b. No

, Question 3 pts


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


a. 0


b. 0.5


c. 1


d. 2


Correct! e. 4




Question 4 pts


If Z1, Z2, ⋯ , Z2n are i.i.d. Nor(0, 1), what is the distribution of
∑2n Z 2 ?
i=1 i


a. Nor(0, 2n)


b. Pois(2n)


orrect n,Answer c. χ2 (2n)


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



e. All of the above.




2/19

, Question 5 pts


Suppose U1 and U2 are i.i.d. Unif(0, 1). What is the distribution of
5U1 − 5U2 ?


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 pts


Suppose U1 and U2 are i.i.d. Unif(0, 1), and let
X = √−2 ln(U1) cos(2πU2). Find Pr(X < −1).

a. 0

Correct! b. 0.1587


c. 0.50


d. 0.8413


e. 1.00




Question 7 n,
pts
n, n, n,



3/19