Suppose I have to vectors $w$ and $x$, each of size $[512,1]$. Each element of $w$ and $x$ is an i.i.d sample from a Guassian Distibution with mean 0 and variance 1. So $x_i$ and $w_i$ follow $N(0,1)$
Let $y=w^Tx$ be my vector of interest. Then the question is what is the variance of $y$?
So $y=\sum w_ix_i$
$Var(y)=\sum Var(w_ix_i)$
I do not know how to take it forward from here....