For two random variable with $E[|X_2|^2]>E[|X_1|^2]$ is it mean $|X_1|^2>|X_2|^2$

Question

for $i\in\{1,2\}$, let $X_i$ Gaussian random variable with mean zero a and variance 1/2. $X_1$ and $X_2$ are independent.

Let $E[|X_1|^2]=\delta_1$ and $E[|X_2|^2]=\delta_2$, where $\delta_2>\delta_1$.

Does this mean

$$|X_2|^2>|X_1|^2$$

always hold or not?

Answer 1

I case $X_1$ and $X_2$ are also independent the inequality $|X_2|^{2} >|X_1|^{2}$ cannot hold. Just use the fact that the joint density is positive at all points of the plane.