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ThmDex – An index of mathematical definitions, results, and conjectures.
Uncorrelated random collection need not be independent
Formulation 0
Let XGaussian(0,1) be a D211: Standard gaussian random real number such that
(i) Y:=X2
Then
(1) EXY=EX3=0
(2) P(X>1,Y<1)=0P(X>1)P(Y<1)
Proofs
Proof 0
Let XGaussian(0,1) be a D211: Standard gaussian random real number such that
(i) Y:=X2
Clear.