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Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 223
/
4
/
b
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2024
iii
Paper 223
4
b
Created
2026-09-24
Updated
2026-09-25
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Define
R
X
(
μ
)
=
sup
∥
v
∥
2
≤
1
∣
MOM
k
(
X
v
)
−
μ
T
v
∣.
(1)
For every unit-ball
vector
v
, the
triangle inequality
gives
∣
v
T
(
μ
−
μ
0
)
∣
≤
∣
MOM
k
(
X
v
)
−
μ
T
v
∣
+
∣
MOM
k
(
X
v
)
−
μ
0
T
v
∣.
(2)
Taking the
supremum
and using optimality,
R
X
(
μ
)
≤
R
X
(
μ
0
)
, yields
∥
μ
−
μ
0
∥
2
≤
R
X
(
μ
)
+
R
X
(
μ
0
)
≤
2
R
X
(
μ
0
)
.
(3)
Ancestors
(11)
b
4
Paper 223
iii
2024
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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