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•
If
X
is exponential with parameter
λ
, show that the ‘ceiling’ of
X
(i.e., the
next integer)
Y
has geometric distribution with parameter
p
= 1

exp(

λ
)
.
Hint: Consider
P
(
Y
= 1) =
P
(0
< X <
1)
, generalize for any
i
, and
compare with the pmf of the geometric which is
P
(
Y
=
i
) =
p
(1

p
)
i

1
.
•
If
X
1
,...,X
n
are exponentially distributed, show that the distribution of
Y
= min(
X
1
,...,X
n
)
is exponential with parameter
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This note was uploaded on 01/16/2011 for the course STAT 213 taught by Professor Ioannam during the Fall '09 term at Duke.
 Fall '09
 IoannaM

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