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ThmDex – An index of mathematical definitions, results, and conjectures.
Definitions
,
Results
,
Conjectures
Result R2100 on
D1719: Expectation
Subresult of
R2014: Triangle inequality for signed basic integral
Triangle inequality for signed basic expectation
Formulation 0
Let
X
∈
Random
[
−
∞
,
∞
]
be a
D4381: Random basic number
such that
(i)
E
|
X
|
<
∞
Then
E
X
≤
|
E
X
|
≤
E
|
X
|
Proofs
Proof 0
Let
X
∈
Random
[
−
∞
,
∞
]
be a
D4381: Random basic number
such that
(i)
E
|
X
|
<
∞
This result is a particular case of
R2014: Triangle inequality for signed basic integral
.
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