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Let ${\bf A} =(a_{ij})$ be an $m\times n$ matrix such that all $a_{ij}$s are real valued independent random variables.

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Also $\mathbb{E}[a_{ij}]=0$ and Var$(a_{ij})=1$. Let ${\bf x}\in \mathbb{R}^n$. Show that $\mathbb{E}[\|{\bf Ax}\|]=m\|{\bf x}\|^2$ where $\|{\bf x}\|^2={\bf x^Tx}$.


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