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Past exam of the mathematics course of the University of Oxford
/
2015
/
Prelims
/
Mathematics III
/
7
/
b
/
iv
/
Solution
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2015
Prelims
Mathematics III
7
b
iv
2026-10-25
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The
recurrence relation
at
k
=
3
gives
I
5
=
2
θ
I
3
=
2
θ
2
. Consequently
var
(
X
i
2
)
=
E
[
X
i
4
]
−
(
E
[
X
i
2
]
)
2
=
I
5
−
I
3
2
=
2
θ
2
−
θ
2
=
θ
2
.
(1)
By
variance additivity for independent random variables
, the
variance
of their
sample mean
is
var
(
θ
)
=
n
2
n
θ
2
=
n
θ
2
.
(2)
Ancestors
(13)
iv
b
7
Mathematics III
Prelims
2015
Past exam of the mathematics course of the University of Oxford
Mathematics course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
University of Oxford
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