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IE 111
NAME
__________________________
10:00 Section
Exam 4
Fall 2007
Instructions
•
Open book, open notes
•
Clearly indicate your answer
•
You must show all relevant work and justify your answers appropriately
•
Partial credit will be given, but not without sufficient support
•
Each question is worth 33.3 points
•
You do not need to interpolate in tables.
Just pick closest value.
40's 2
Mean
76.2
50's 6
StDev
13
60's 0345778
N
29
70's 0155779
Med
77
80's 000126799
90's 2469
100's
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Consider the following joint distribution of X and Y:
X
0
1
Y
0
0
0.6
1
0.4
0
a)
Find the marginal distributions of X and Y
f(x)
f(y)
P(X=0) = 0.4
P(Y=0) = 0.6
P(X=1) = 0.6
P(Y=1) = 0.4
b)
Find E(X) and E(Y)
E(X) = 0*0.4+1*0.6 = 0.6
E(Y) = 0.4
c)
Find V(X) and V(Y)
E(X
2
) = 0.6
⇒
V(X) = 0.6(0.6)
2
=
0.24
E(Y
2
) = 0.4
⇒
V(Y) = 0.4(0.4)
2
=
0.24
d)
Find COV(X,Y)
COV(X,Y) = (10.6)(00.4)(0.6) + (00.6)(10.4)(0.4) =
0.24
e)
Find the correlation
ρ
xy
1
)
24
.
0
)(
24
.
0
(
24
.
0

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This homework help was uploaded on 02/26/2008 for the course IE 111 taught by Professor Storer during the Spring '07 term at Lehigh University .
 Spring '07
 Storer

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