(adsbygoogle = window.adsbygoogle || []).push({}); Hi,

I am having a hard time understanding why the Addition Rule for two Random Variables holds even when the random variables are dependent.

Essentially: why is E(X+Y) = E(X) + E(Y) when X and Y are dependent random variable?

Given the two variables are dependent, if X happens to take on a valuex, for example, doesn't that change the probability distribution ofYand, thus, affect its expected value?

I hope I made my doubt clear,

Best,

Peter G.

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# Addition Rule for Random Variables

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