Exam2 yes
Data analytics (University of
Georgia)
, 1
ISyE 6644 — Test #2 Solutions
(revised 10/26/20)
This test is 120 minutes. The first 22 questions are each worth 3 points. The following
17 questions (all Arena) are each worth 2 points.
Let’s get some lawyer stuff out of the way. . .
You’re allowed the following items:
• Pencil / pen and scratch paper.
• A reasonable calculator.
• Two cheat sheets (4 sides total).
2
• Normal, t, and χ tables. (I will supply these.)
But note that
• You are not allowed to use Arena, even though I’m asking questions about it.
• This test requires some sort of proctor.
• If you encounter a ProctorTrack issue, contact us immediately (but don’t get an
ulcer over it).
Good luck! I want you to make this test sorry that it ever tried to mess around with
you!!!
1. Consider the following joint p.m.f.
f (x, y) X = 1 X = 2 fY (y)
Y =0 0.4 0.2 0.6
Y =1 0.1 0.3 0.4
fX(x) 0.5 0.5 1.0
Let X represent how many times you watch Netflix in a week and let Y represent
the number of times you miss your bus to work in a week (note that you always
watch Netflix at least once).
YES or NO? Are watching Netflix and missing the bus independent?
Solution: Note that f (1, 0) = 0.4/ = (0.5)(0.6) = fX(1)fY (0). Thus, the answer
is NO. □
, 2
2. Again consider the following joint p.m.f.
f (x, y) X = 1 X = 2 fY (y)
Y =0 0.4 0.2 0.6
Y =1 0.1 0.3 0.4
fX(x) 0.5 0.5 1.0
Find Cov(X, Y ).
(a) −1
(b) −0.1
(c) 0
(d) 0.1
(e) 2
Solution: The table immediately gives us
Σ
E[X] = xfX(x) = 1(0.5) + 2(0.5) = 1.5
x
Σ
E[Y ] = yfY (y) = 0(0.6) + 1(0.4) = 0.4
y
Σ Σ
E[XY ] = xyf (x, y)
x y
= 1(0)(0.4) + 2(0)(0.2) + 1(1)(0.1) + 2(1)(0.3) = 0.7.
Thus,
Cov(X, Y ) = E[XY ] − E[X]E[Y ] = 0.7 − (1.5)(0.4) = 0.1.
So the answer is (d). □
3. TRUE or FALSE? Most discrete-event simulations proceed by moving the
simulation clock to the most-computationally-intensive event on the future events
list, i.e., the event that takes the “most work” to deal with; executing that
event (including any adds, deletes, or swaps to the FEL); and then repeating this
cycle.
Solution: FALSE. The simulation clock moves to the most-imminent event. □
Data analytics (University of
Georgia)
, 1
ISyE 6644 — Test #2 Solutions
(revised 10/26/20)
This test is 120 minutes. The first 22 questions are each worth 3 points. The following
17 questions (all Arena) are each worth 2 points.
Let’s get some lawyer stuff out of the way. . .
You’re allowed the following items:
• Pencil / pen and scratch paper.
• A reasonable calculator.
• Two cheat sheets (4 sides total).
2
• Normal, t, and χ tables. (I will supply these.)
But note that
• You are not allowed to use Arena, even though I’m asking questions about it.
• This test requires some sort of proctor.
• If you encounter a ProctorTrack issue, contact us immediately (but don’t get an
ulcer over it).
Good luck! I want you to make this test sorry that it ever tried to mess around with
you!!!
1. Consider the following joint p.m.f.
f (x, y) X = 1 X = 2 fY (y)
Y =0 0.4 0.2 0.6
Y =1 0.1 0.3 0.4
fX(x) 0.5 0.5 1.0
Let X represent how many times you watch Netflix in a week and let Y represent
the number of times you miss your bus to work in a week (note that you always
watch Netflix at least once).
YES or NO? Are watching Netflix and missing the bus independent?
Solution: Note that f (1, 0) = 0.4/ = (0.5)(0.6) = fX(1)fY (0). Thus, the answer
is NO. □
, 2
2. Again consider the following joint p.m.f.
f (x, y) X = 1 X = 2 fY (y)
Y =0 0.4 0.2 0.6
Y =1 0.1 0.3 0.4
fX(x) 0.5 0.5 1.0
Find Cov(X, Y ).
(a) −1
(b) −0.1
(c) 0
(d) 0.1
(e) 2
Solution: The table immediately gives us
Σ
E[X] = xfX(x) = 1(0.5) + 2(0.5) = 1.5
x
Σ
E[Y ] = yfY (y) = 0(0.6) + 1(0.4) = 0.4
y
Σ Σ
E[XY ] = xyf (x, y)
x y
= 1(0)(0.4) + 2(0)(0.2) + 1(1)(0.1) + 2(1)(0.3) = 0.7.
Thus,
Cov(X, Y ) = E[XY ] − E[X]E[Y ] = 0.7 − (1.5)(0.4) = 0.1.
So the answer is (d). □
3. TRUE or FALSE? Most discrete-event simulations proceed by moving the
simulation clock to the most-computationally-intensive event on the future events
list, i.e., the event that takes the “most work” to deal with; executing that
event (including any adds, deletes, or swaps to the FEL); and then repeating this
cycle.
Solution: FALSE. The simulation clock moves to the most-imminent event. □
