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Hoeffding inequality
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Mathematics
Area of mathematics
Probability and statistics
Probability theory
Probability inequality
Concentration inequality
2026-09-24
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If
independent random variables
satisfy
a
i
≤
X
i
≤
b
i
, then
P
(
∑
i
(
X
i
−
E
X
i
)
≥
t
)
≤
exp
(
−
∑
i
(
b
i
−
a
i
)
2
2
t
2
)
,
(1)
with the same bound for the lower tail.
Table of contents
Hoeffding lemma
Hoeffding inequality
Hoeffding lemma
0
0
0
Hoeffding inequality
If
a
≤
X
≤
b
almost surely
, then
lo
g
E
e
λ
(
X
−
E
X
)
≤
8
λ
2
(
b
−
a
)
2
.
(1)
Ancestors
(7)
Concentration inequality
Probability inequality
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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(2)
Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 205
/
3
/
d
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 208
/
1
/
c
/
Solution
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