Expected value of a random variable and its square root

Asked Jun 29 '15 at 15:50

Active Jun 29 '15 at 15:50

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Can the expectation of a random variable be written in this fashion: $$E(\sqrt{X} + X) = E(\sqrt{X}) + E(X)$$ Thanks in advance

asked Jun 29 '15 at 15:50

Joz

3

Expectation is linear and hence for any random variables $X, Y$ and real constants $a, b$:
$$E[aX + bY] = aE[X] + bE[Y]$$
– Simon S Jun 29 '15 at 15:52
I suppose you are saying yes! – Joz Jun 29 '15 at 15:58

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