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Order Statistics
Order Statistics
5 selected
Difficulty 3-7
5 unseen
View topic
Foundation
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0 answered
1 foundation
3 intermediate
1 advanced
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Question 1 of 5
120s
foundation (3/10)
compute
For
X
1
,
…
,
X
n
i.i.d. Uniform
(
0
,
1
)
, what is
E
[
X
(
n
)
]
, the expected value of the maximum?
Hide and think first
A.
E
[
X
(
n
)
]
=
n
/
(
n
+
1
)
, the mean of a Beta
(
n
,
1
)
density, approaching
1
as
n
→
∞
without ever reaching it.
B.
E
[
X
(
n
)
]
=
1
for all
n
, because the maximum of uniforms equals the upper endpoint of the support in expectation.
C.
E
[
X
(
n
)
]
=
(
n
−
1
)
/
n
, by analogy with the unbiased estimator for the upper endpoint of a uniform distribution.
D.
E
[
X
(
n
)
]
=
1/2
, since the maximum of uniforms is symmetric around the midpoint of the unit interval.
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