scratch
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Mean, Variance And Everything Else As Geometry
created 2026-08-12 · last edited 2026-08-28
Video
Space of vectors, where random varibles are vectors with coefficients given by the realization, and the all-ones vector is the RV
1
1
1
.
Inner product given by
⟨
X
,
Y
⟩
=
E
[
X
Y
]
\langle X, Y \rangle = E[XY]
⟨
X
,
Y
⟩
=
E
[
X
Y
]
.
This gives
⟨
X
,
1
⟩
=
E
[
X
]
\langle X, 1 \rangle = E[X]
⟨
X
,
1
⟩
=
E
[
X
]
.
Roman Paolucci: Ito's Lemmas
Roman Paolucci: Ito Integration
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