IE 111
NAME
__________________________
9:00 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 355
StDev
13.5
60's 489
N
27
70's 0466788889
Med
77
80's 336789
90's 002
100's 0
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View Full DocumentQuestion 1
Consider the (trivariate or “three variable”) joint distribution of random variables X, Y,
and Z given below.
Z=0
Z=1
X=0
X=1
X=0
X=1
Y=0
0
0.3
Y=0
0.1
0
Y=1
0.2
0
Y=1
0
0.15
Y=3
0
0.1
Y=3
0.15
0
a)
What is the marginal distribution of X?
P(X=0) = 0+0.2+0+0.1+0+0.15 = 0.45
P(X=1) = 0.3+0+0.1+0+0.15+0 = 0.55
b)
Find the (bivariate or “two variable”)
joint distribution between X and Z
Just sum over Y:
X=0
X=1
Z=0
0.2
0.4
Z=1
0.25
0.15
c)
Find E(XY=0)
The conditional joint distribution of X and Z given Y=0, P(x,yz) is
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 Spring '07
 Storer
 Probability theory, Discrete probability distribution, Marginal distribution, Z=1 X=0

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