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Proof of expected value....?
I need to prove that E[X+Y]=E[X]+E[Y] for two cases:
i)X and Y are independent
ii)general case--no independence
A proof or a link to such a proof would be great.
1 Answer
- 1 decade agoFavorite Answer
Hmm, that's interesting. I guess I've never seen an actual proof of that. All you need to do is remember that expected value is an integral, integral is a linear operator, so expectation is a linear operator.
The dependence of X and Y plays no part in the integral because integration is linear. You can just separate the parts of the summation into separate integrals and evaluate them individually.
