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Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 207
/
6
/
a
/
iv
/
Solution
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2023
iii
Paper 207
6
a
iv
2026-09-28
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With
cause-specific hazards
h
A
and
h
B
, survival
free
of either
event
through
time
u
is
S
(
u
)
=
exp
[
−
∫
0
u
{
h
A
(
s
)
+
h
B
(
s
)}
d
s
]
.
(1)
The
probability
of remaining
event
-
free
to
u
and then experiencing
A
in
d
u
is
S
(
u
)
h
A
(
u
)
d
u
. Therefore
F
A
(
t
)
=
∫
0
t
exp
[
−
∫
0
u
{
h
A
(
s
)
+
h
B
(
s
)}
d
s
]
h
A
(
u
)
d
u
.
(2)
Ancestors
(12)
iv
a
6
Paper 207
iii
2023
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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