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International Scholarly Research Notices
/
2012
/
Article
/
Tab 8
/
Research Article
On the Order Statistics of Standard Normal-Based Power Method Distributions
Table 8
Expected values of order statistics for
𝑝
3
(
𝑍
)
=
(
4
/
4
3
)
𝑍
5
for
𝑛
=
6
,
7
.
𝐸
[
𝑝
3
(
𝑍
)
4
∶
6
√
]
=
1
0
3
4
3
𝜋
5
/
2
+
3
8
5
√
1
2
9
2
𝜋
3
/
2
−
√
1
9
2
5
2
t
a
n
−
1
√
(
3
3
/
2
/
7
)
1
2
9
𝜋
5
/
2
+
𝐸
[
𝑝
1
(
𝑍
)
4
∶
6
]
=
0
.
0
2
0
4
5
2
1
6
…
𝐸
[
𝑝
3
(
𝑍
)
5
∶
6
5
√
]
=
−
3
4
3
𝜋
5
/
2
−
3
8
5
√
1
2
9
2
𝜋
3
/
2
+
√
1
9
2
5
2
t
a
n
−
1
√
(
3
3
/
2
/
7
)
√
1
2
9
2
𝜋
5
/
2
+
𝐸
[
𝑝
1
(
𝑍
)
5
∶
6
]
=
0
.
1
6
3
8
1
2
8
4
…
𝐸
[
𝑝
3
(
𝑍
)
6
∶
6
√
]
=
3
4
3
𝜋
5
/
2
+
3
8
5
√
1
2
9
2
𝜋
3
/
2
−
3
8
5
t
a
n
−
1
√
(
3
3
/
2
/
7
)
√
1
2
9
2
𝜋
5
/
2
+
𝐸
[
𝑝
1
(
𝑍
)
6
∶
6
]
=
1
.
5
9
0
1
9
0
6
1
…
𝐸
[
𝑝
3
(
𝑍
)
4
∶
7
]
=
0
𝐸
[
𝑝
3
(
𝑍
)
5
∶
7
√
]
=
3
5
3
8
6
𝜋
5
/
2
+
2
6
9
5
√
5
1
6
2
𝜋
3
/
2
−
1
3
4
7
5
t
a
n
−
1
√
(
3
3
/
2
/
7
)
√
2
5
8
2
𝜋
5
/
2
+
𝐸
[
𝑝
1
(
𝑍
)
5
∶
7
]
=
0
.
0
3
5
7
9
1
2
8
…
𝐸
[
𝑝
3
(
𝑍
)
6
∶
7
√
]
=
−
1
4
3
4
3
𝜋
5
/
2
−
2
6
9
5
√
2
5
8
2
𝜋
3
/
2
+
√
2
6
9
5
2
t
a
n
−
1
√
(
3
3
/
2
/
7
)
1
2
9
𝜋
5
/
2
+
𝐸
[
𝑝
1
(
𝑍
)
6
∶
7
]
=
0
.
2
1
5
0
2
1
4
6
…
𝐸
[
𝑝
3
(
𝑍
)
7
∶
7
7
√
]
=
3
8
6
𝜋
5
/
2
+
2
6
9
5
√
5
1
6
2
𝜋
3
/
2
−
2
6
9
5
t
a
n
−
1
√
(
3
3
/
2
/
7
)
√
2
5
8
2
𝜋
5
/
2
+
𝐸
[
𝑝
1
(
𝑍
)
7
∶
7
]
=
1
.
8
1
9
3
8
5
4
6
…
