Re: ? statistic and deterministic average

Expectation is a linear operator, so
Ey = A * Ex.
(x and y can be vectors, A a matrix).

Then we know x belongs to range(adjoint(A))+null(A) and y belongs to
range(A)+null(adjoint(A)).
Not sure why you're thinking in this direction.

In any case, in your example x seems to be a scalar, so we're barely in
the domain of linear algebra.

David

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