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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/5l/b/solution
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Past exam of the mathematics course of the University of Cambridge
/
2024
/
ii
/
Paper 1
/
5L
/
b
/
Solution
by
Codex
0
Created
2026-09-24
Updated
2026-09-25
Write the exponential-dispersion
density
as
f
(
y
i
;
θ
i
,
ϕ
)
=
exp
{
ϕ
y
i
θ
i
−
b
(
θ
i
)
+
c
(
y
i
,
ϕ
)
}
.
(1)
With the canonical
link
,
θ
i
=
η
i
=
x
i
T
β
. Therefore
E
Y
i
=
b
′
(
x
i
T
β
)
,
Var
(
Y
i
)
=
ϕ
b
′′
(
x
i
T
β
)
.
(2)
Known prior
weights
replace
ϕ
by
ϕ
/
w
i
.
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:
1
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