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EXAM P QUESTIONS OF THE WEEK
S. Broverman, 2005
Week of January 23/06
\
]
"ŸBŸ"
#ŸCŸ#
and
have a joint distribution on the twodimensional region
,
,
and the pdf of the joint distribution is
(constant) on the region.
0ÐBßCÑ œ 
Find the probability
.
TÐ
l\lŸl]lÑ
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View Full Document Week of January 23/06  Solution
Whenever a joint distribution has a constant density over the entire probability space
, the
W
probability of any subregion
is equal to
.
E
Area of
Area of
E
W
The area of the full probability space is
(the area of a rectangle with sides that are 2.
#‚%œ)
The graph of the region defined by
is the shaded region illustrated below
l\lŸl]l
To find this region, we first find the boundary
, which is the combination of the two
l\lœl]l
lines
and
. We then determine "which sides" of the lines represent the
CœB
Cœ B
inequality.
Alternatively, we consider the relationship between
and
in the four quadrants:
BC
(i) 1st quadrant,
so
and the inequality becomes
,
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This note was uploaded on 03/29/2010 for the course STATISTICS 50 taught by Professor Diaz during the Spring '10 term at California State University , Monterey Bay.
 Spring '10
 Diaz
 Probability

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