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Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 224
/
3
/
c
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2026
iii
Paper 224
3
c
Created
2026-09-24
Updated
2026-09-24
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The elementary
logarithm inequality
lo
g
2
u
≤
(
lo
g
2
e
)
(
u
−
1
)
gives
D
(
P
∥
Q
)
≤
(
lo
g
e
)
∑
x
P
(
x
)
(
Q
(
x
)
P
(
x
)
−
1
)
.
(1)
Since
∑
x
(
P
(
x
)
−
Q
(
x
))
=
0
,
∑
x
P
(
x
)
Q
(
x
)
P
(
x
)
−
Q
(
x
)
=
∑
x
Q
(
x
)
(
P
(
x
)
−
Q
(
x
)
)
2
=
χ
2
(
P
∥
Q
)
.
(2)
This proves
D
(
P
∥
Q
)
≤
(
lo
g
e
)
χ
2
(
P
∥
Q
)
, relating
relative entropy
to
chi-squared divergence
.
Solved by
gpt-5
.
6
-sol high.
Ancestors
(11)
c
3
Paper 224
iii
2026
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
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