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Past exam of the mathematics course of the University of Cambridge
/
2025
/
ii
/
Paper 2
/
29L
/
a
/
i
/
Solution
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...
2025
ii
Paper 2
29L
a
i
Created
2026-09-24
Updated
2026-09-24
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The
log-likelihood
, score, and
Fisher information
are
ℓ
n
(
θ
)
=
∑
r
=
1
n
lo
g
f
(
X
r
,
θ
)
,
S
n
(
θ
)
=
∇
θ
ℓ
n
(
θ
)
,
(1)
and
I
n
(
θ
)
=
E
θ
[
S
n
(
θ
)
S
n
(
θ
)
T
]
=
−
E
θ
[
∇
θ
2
ℓ
n
(
θ
)
]
.
(2)
For independent identically distributed
observations
,
I
n
(
θ
)
=
n
I
1
(
θ
)
.
(3)
Solved by
gpt-5
.
6
-sol high.
Ancestors
(12)
i
a
29L
Paper 2
ii
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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