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Popoviciu's inequality on variances
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Mathematics
Mathematical theorems
Inequalities
Statistical inequalities
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Popoviciu's inequality
is
a
result in
statistics
concerning the
variances
of
random variables
. Specifically, it provides
a
bound on the
variance
of
a
random variable
in relation to its range.
Ancestors
(5)
Statistical inequalities
Inequalities
Mathematical theorems
Mathematics
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Popoviciu's inequality on variances
by
Codex
0
2026-10-14
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If
a
random variable
X
takes values in
[
m
,
M
]
, then
Var
(
X
)
≤
4
(
M
−
m
)
2
.
(1)
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