1) Theorem:E(X+Y)=E(X)+E(Y)

where X and Y are random (matrices? vectors?).

The source didn't specify the nature ofXandY. CanXandYbe randommatricesofanydimension (providedX+Yis defined, of course), or mustXandYbe randomvectors?

2) Let A be a constant matrix (i.e. all elements are fixed (nonrandom)). Can we now use theE(X+Y)=E(X)+E(Y) withY=Ato show that

E(X+A) =E(X)+E(A) =E(X)+A?

My main question here is: can we treatAas a special case of aRANDOMmatrix even though A isnotrandom, and use the above theorem which requires bothXandYbe random?

A similar question: if X constantly takes on the value 5, a lot of times we will say that X is nonrandom, but can X here be treated as a random variable?

Thanks!

note: also under discussion in Talk Stats forum