Processing math: 100%
ThmDex – An index of mathematical definitions, results, and conjectures.
Definitions
,
Results
,
Conjectures
Result R3833 on
D2713: Independent random collection
Uncorrelated random collection need not be independent
Formulation 0
Let
X
∼
Gaussian
(
0
,
1
)
be a
D211: Standard gaussian random real number
such that
(i)
Y
:=
X
2
Then
(1)
E
X
Y
=
E
X
3
=
0
(2)
P
(
X
>
1
,
Y
<
1
)
=
0
≠
P
(
X
>
1
)
P
(
Y
<
1
)
Proofs
Proof 0
Let
X
∼
Gaussian
(
0
,
1
)
be a
D211: Standard gaussian random real number
such that
(i)
Y
:=
X
2
Clear.
◻