Talk:Algebra of random variables

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Needs radical repair

As of January 2013, this article is in urgent need of a complete rewrite. The article mixes exposition at several different levels of sophistication, and makes several serious blunders. This degree of confusion is unacceptable in a mathematical Wikipedia article. —Aetheling (talk) 07:16, 5 January 2013 (UTC)[reply]

January 2013 according to the signature. =P Anyway, I agree and I've tagged it appropriately to hopefully increase its visibility in relevant cleanup categories and the Statistics WikiProject. To document my own reasoning with regard to the tags: the article provides very little general context and discussion accessible to someone who's unfamiliar with it, nor a solid or well-organized overview, nor even any kind of summary in the lead paragraph. It dives into various details and, as the above user said, mixes information at different levels of mathematical sophistication to the point that it's utterly impossible to follow without having a solid background already. Laogeodritt ^{[ Talk | Contribs ]} 17:25, 3 February 2013 (UTC)[reply]

von Neumann algebra

Shouldn't the *-algebra be a Von Neumann algebra to take into account infinite dimensional spaces?

Conditional expectation

Is there a similar axiomatization for conditional expectation? -- Spireguy (talk) 02:36, 26 March 2010 (UTC)[reply]

One definition of the quantum (non-commutative) version of a conditional expectation is

"Let there be a quantum probability space (N,ρ) and a commutative von Neumann sub-algebra C ⊂ N. Then the quantum conditional expectation π( · ) is a map from C′ (the commutant of C) to C such that ρ (π(X)Z) = ρ (XZ) for all X ∈ C′, Z ∈ C."

So I'd hazard a guess that an appropriate algebraic definition for the (commutative) conditional expectation would be

"If N is the algebra of all random variables considered, and C is a (von Neumann) sub-algebra (relating to the measurement outcome), then the conditional expectation is a map P from N to C such that E[P(X)Z] = E[XZ] for all X in N and Z in C"

Thoughts? -- S.Wilson (talk) 10:46, 9 May 2011 (UTC)[reply]

Rules for variance

Could someone (who knows for sure) add the rules for variance on random variables. E.g.:

Var(c*X) = c*Var(x)

213.165.179.229 (talk) 18:50, 10 July 2011 (UTC)[reply]