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- What is the use of the MSE (Mean Square Error) i.e. why do we use it?

I understand that MSE(t) = Var(t) + {E(t-&)}^2, but what does this tell us?

- Why/ How does E{A*Sx^2 +b*Sy^2} = a*Var + b*Var

(I am using ^ to denote 'powers' i.e. '^2' means sqaured)

- What is the E(-) operator, what is its use and what are its properties.

I would really, really appreciate help on this as I am having difficulties grasping these concepts of statistical theory.

Thanks