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Problem 1. Let X,Y,Z be independent random variables where X,Y are uniformly distributed on [0 , 1] and Z is an exponential with mean 1.
Problem 1.
Let
X,Y,Z
be independent random variables where
X,Y
are uniformly distributed
on
[0
,
1]
and
Z
is an exponential with mean 1.
(a) What is the conditional density of
X
given
XY
=
t
for
0
t
1
?
(b) What is the conditional density of
X
given
X
+
Z
=
t
for
t
0
?
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