? statistic and deterministic average

Hi:

Suppose we have a random variable x with a distribution f(x), its average
or expectation

is defined as E[x] = Integral( x*f(x), x = -inf...inf )

Now, suppose we have a linear map A that maps a DETERMINISTIC variable x to
y, that is:

y = A*x

Then we know x belongs to range(adjoint(A))+null(A) and y belongs to
range(A)+null(adjoint(A)).

In this case, what is the "expection" or average of x?

Thanks,
by Cheng Cosine
Mar/11/2k6 NC




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