Is $$E(\sum X^3)=\sum E(X^3)$$ I think that it shouldn't be true because $$\sum X^3$$ is just a number and how to find expectation of it?
2026-03-27 07:20:18.1774596018
Basic Probability expectation
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It is true, since expectation is linear. I.e., if $X,Y$ are random variables, and $\alpha, \beta$ are scalars, then $$E[\alpha X + \beta Y] = \alpha E[X] + \beta E[Y]$$
provided of course that both $X,Y$ have an expectation ("$X$ and $Y$ are integrable").