Consider a random variable $X$ defined on the probability space $(\Omega, \mathcal{F}, \mathbb{P})$, $X: \Omega \rightarrow \mathbb{R}$.
(1) If $\exists$ $E_{\mathbb{P}}(X)$, then $$ \mathbb{P}(|X|\geq t)\leq \frac{E_{\mathbb{P}}(|X|)}{t} $$
$\forall t>0$ (Markov inequality). Question: do we need $|E_{\mathbb{P}}(X)|<\infty$ to show the result? I think the answer is no, but I would like a confirmation.
(2) If $\exists$ $Var(X)$, then $$ \mathbb{P}(|X-E_{\mathbb{P}}(X)|\geq t)\leq \frac{Var(X)}{t^2} $$
$\forall t>0$ (Chebychev inequality). Question: do we need $Var(X)<\infty$ to show the result? I think the answer is no, but, again, I would like a confirmation.