Exercise 4.3.15

When $A$ has 1 column of 4 ones, Problem 14 gives the expected error ${(\hat{x}-x)}^2$ as ${\sigma }^2{\left(A^{T}A\right)}^{-1}={\sigma }^2∕4$. By taking $m$ measurements, the variance drops from ${\sigma }^2$ to ${\sigma }^2∕m$. This leads to the Monte Carlo method in Section 12.1.