Re: Expected value theorem

In article <3718694.1162847642987.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
guest101 <guest101@xxxxxxxxx> wrote:
Hello,

Thanks again for the reply

I'm trying to prove that:
E[X+Y] = E[X] + [Y]

for all Real numbers that are random variables

Do I use X = X^+ - X^- and Y = Y^+ - Y^-
in the solution?

I'm honestly completely lost, I know the definition of expectation but am unable to apply it here. I'm sure the solution is very small and trivial so I'd honestly appreciate any more help.

Thank you

I am not sure what "definition" of expectation you have
seen, but most are next to impossible to prove the result.

For any countably (finitely) additive elementary integral
phi, define f to be integrable if for every epsilon > 0,
there exists a g and there exist a sequence ofnon-negative
elementarily integrable functions h_i (finite instead of
a sequence for finite additivity) such that

|f - g| <= sum h_i
sum (phi(h_i)) < epsilon.

This, and easy extensions, covers a lot, and makes the proofs
of what you are trying to do easy. It is also the way
expectations are used, including for vector spaces, complex
functions, etc.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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