How to define an expectation operator

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Is there a way to define as a new operator the mathematical expectation.

Say we call it $\mathrm{M}$ as in the old Mir (russian books).

We should have

$\mathrm{M}(kX) = k\mathrm{M}(X)$

$\mathrm{M}(X \pm Y) = \mathrm{M}(X)\pm \mathrm{M}(Y)$

and as a résult

$\mathrm{M}(X -\mathrm{M}X)^2 =\mathrm{M}(X^2)- \mathrm{M}(X)^2$

and other result for variances and covariances