3 ms·
> You say variance covariance etc etc, but it does not take much for RVs not to possess them In practice, essentially always, for real random variables X, Y,
by graycat 9y ago
> You say variance covariance etc etc, but it does not take much for RVs not to possess them
In practice, essentially always, for real random variables X, Y, all of the
following exist and are finite:
E[X], E[|X|], E[X^2],
E[XY]
Var(X) = E[(X - E[X])^2]
Std(X) = Var(X)^(1/2)
Cov(X,Y) = E[(X - E[X])
(Y - E[Y])]
Cor(X,Y) = Cov(X,Y)/(Std(X) Std(Y))
E[Y|X]
E[X] and Std(X)are
useful quite broadly and
that we find/estimate them
does not mean that we
are working with a Gaussian
distribution.
If the above is not true,
then there is something
bizarre and/or pathological,
the ultimate edge case, and
we need to review what
we are doing.
- srean 9y agoUnfortunately its not true in many cases I have seen, essentially because the tail of the error does not fall fast enough. Technically, for all bounded RVs all moments are bounded, but in some of these situations the variance is so high that its infinite for practical purposes. All you need is the tail to fall slower than a quadratic.