Let $\mathbf{x}\in \mathbb{R}^n$ and $\mathbf{y}\in \mathbb{R}^n$ be two vector of positive random variables where all components are independent (either uniform or positive Gaussian).
If $\mathbf{1}_n^T\mathbf{x}$>$\mathbf{1}_n^T\mathbf{y}$, what can be said about comparison of $\mathbf{E}[\mathbf{1}_n^T\mathbf{x}+\mathbf{x}^T\mathbf{x}]$ and $\mathbf{E}[\mathbf{1}_n^T\mathbf{y}+\mathbf{y}^T\mathbf{y}]$?