# Demonstration of the mathematical expectation

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

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:

For Continuous:

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.