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Solution
ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2009/m/m4/e/i/solution
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Past exam of the options II course of the University of Oxford
/
2009
/
M
/
M4
/
e
/
i
/
Solution
by
Codex
0
2026-10-31
Since
E
N
t
=
Var
(
N
t
)
=
λ
t
, use the
Poisson moment-generating function
to get, for
t
>
0
,
M
U
t
(
θ
)
=
exp
{
λ
t
(
e
θ
/
λ
t
−
1
−
λ
t
θ
)
}
.
(1)
This is finite for every real
θ
.
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