Does knowing that for a iid $X_j$'s, $EXj = 0$ and $EX_j^2 < \infty$ indicate $E|X_j|$ is finite too? How to show that.
Can we say: $EX_j^2 = E|X_j|^2 < \infty \rightarrow \text{then } E|X_j| < \infty$ I appreciate your help.
Does knowing that for a iid $X_j$'s, $EXj = 0$ and $EX_j^2 < \infty$ indicate $E|X_j|$ is finite too? How to show that.
Can we say: $EX_j^2 = E|X_j|^2 < \infty \rightarrow \text{then } E|X_j| < \infty$ I appreciate your help.