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If $X,Y$ are random variables, what is the name of the term $E(XY)$? (which if we subtract $E(X)E(Y)$ gives the covariance)

user56834
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1 Answers1

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Moments of the form $\mu'_{rs}=E(X^rY^s)$ are called "product moments" or more specifically "$r,s$ product moments"; you have the $1,1$ product moment, $\mu_{11}$. They may also be called raw product moments (to distinguish from central ones like covariance).

Some people might call it a 'first order product moment', though 'first order' can be somewhat ambiguous (some people might interpret that to mean $\mu_{01}$ or $\mu_{10}$, perhaps).

They are also sometimes called mixed moments (since they involve more than one variable) but the term can apply to moments in more than two variates; in this case we have mixed raw moments.

Glen_b
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  • I have also heard people call $\mu_{rs}$ the $(r,s)$th order bivariate moment/product moment about zero. They denote it by $\mu_{r,s}'$. – StubbornAtom May 18 '18 at 05:47
  • Isnt there an abbreviation for the 1,1 moment? Similar to "mean" for the first moment? – user56834 May 18 '18 at 06:11
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    @StubbornAtom I should have a ' on $\mu_{rs}$ there (but not on $\mu_{1,1}$) – Glen_b May 18 '18 at 12:31
  • @Programmer2134 There's going to be several names, I think. Did you have a particular name in mind? – Glen_b May 18 '18 at 12:32
  • If I had a name in mind I wouldnt have asked this question – user56834 May 18 '18 at 14:53
  • Sorry, it just sounded like maybe you already had an idea of what it might be from your comment (more of an idea than was in your comment). There will be names for it that I don't have here (including perhaps simpler or more evocative terms than I've used); I'm dragging terms up out of memory and putting them in when they come to me (I haven't had to put a name to these in decades). I figured if you had part of a term or some notion about it (maybe you thought you remembered the first letter or something) that it might jog the memory better. – Glen_b May 18 '18 at 22:59
  • Oh that makes sense. Well hmm, not really. I was thinking about something like cross-mean or something like that – user56834 May 19 '18 at 02:13