For \(n=100\) points \(t_{1}, \ldots, t_{n}\) equally spaced in the interval \((0,48)\), compute the matrix

\[
\Sigma_{i j}=\delta_{i j}+\theta\left(t_{i} \wedge t_{j}ight)
\]

for small values of \(\theta\), say \(0 \leq \theta \leq 0.02\). Find the maximum-likelihood estimate of \(\beta\) in the linear model \(Y \sim N_{n}(\alpha+\beta t, \Sigma)\) with \(\Sigma\) known, and plot the variance of \(\hat{\beta}\) as a function of \(\theta\). Comment on the effect of the Brownian-motion component.