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I'm studying for my exam of probability distributions and in my study book got these equalities for the expectation:

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I thought of using any of the two definitions to find the expectation of a random variable (continuous or discrete) but I can not reach that conclusion.

For Discrete: enter image description here

For Continuous: enter image description here

This property is true?, How I can get your deduction?

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You get it because $\mathsf E[X]$ is just a constant, and constant is always equal to its expectation.

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    Yes, I $n$oticed shortly after posting the question, thank you very $m$uch for taking the time to respond.2011-11-11