Assume that the input signal is a white noise process with variance $\sigma_x^2$, and the desired response is $d(n) = \alpha x(n) + v(n)$, where $v(n)$ is a white noise process with variance $\sigma_v^2$, independent of $x(n)$. Find the expression for the mean weight update, $E[\mathbfw(n+1)]$, in terms of $E[\mathbfw(n)]$, $\mu$, $\alpha$, $\sigma_x^2$, and $\sigma_v^2$.
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