Expected value of squared random variable if expected value of random variable is $0$

Question

Let

$E[X]=0$

them How is Expected value of $E[X^2]$ ? in my opinion is $0$ But I need confirmation and explanation

In general, if $ (\Omega,\Sigma,P) $ is a probability space and $ X: (\Omega,\Sigma) \to (\mathbb{R},\mathcal{B}(\mathbb{R})) $ is a real-valued random variable, then $$ \text{E}[X^{2}] = \int_{\Omega} X^{2} ~ d{P}. $$

see for more about this in this quetion Computing the Expectation of the Square of a Random Variable: $E[X^2]$.

Answer 1

No way. Since $X^2\geq 0$, $\mathbb{E}[X^2]=0$ iff $X$ is zero almost surely.

Otherwise, if $\mathbb{E}[X^2]$ is well defined, $\mathbb{E}[X^2]\color{red}{>}0.$