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EXAM P QUESTIONS OF THE WEEK
S. Broverman, 2005
Week of January 30/06
\]
and
are independent continuous random variables. They have the same distribution
functions,
for
and
for
.
J Ð>Ñœ"
>"
""
>>
We define two new random variables
and
as follows:
[^
[ œ 738Ö\ß ] ×
^ œ 7+BÖ\ß ] ×
and
.
Find the mean of
and the mean of
.
The solution can be found below.
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View Full DocumentWeek of January 30/06  Solution
The pdf of
is
and the pdf of
is the same,
.
\
0 Ð>Ñ œ J Ð>Ñ œ
ß
]
0 Ð>Ñ œ
\]
\
w
""
>>
#
#
The pdf of
is
. We can find the pdf of
as follows.
[0
Ð
>
Ñ
œ
J
Ð
>
Ñ
[
[
[
w
J Ð>ÑœTÒ[ Ÿ>
ÓœTÒ738Ö\Þ]×Ÿ>
Óœ"TÒ738Ö\ß]×>
Ó
[
œ"TÒÐ\>Ñ∩Ð] >Ñ
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