Write a program in \(\mathrm{R}\) that generates \(b\) samples of size \(n\) from a \(\mathbf{N}\left(\mathbf{0}, \boldsymbol{\Sigma}_{n}ight)\) distribution where

\[\boldsymbol{\Sigma}_{n}=\left[\begin{array}{cc} 1+n^{-1} & n^{-1} \\ n^{-1} & 1+n^{-1}\end{array}ight]\]

Transform each of the \(b\) samples using the bivariate transformation

\[g\left(x_{1}, x_{2}ight)=\frac{1}{2} x_{1}+\frac{1}{4} x_{2}\]

and produce a histogram of the resulting transformed values. Run this simulation for \(n=10,25,50\), and 100 with \(b=10,000\) and discuss how this histogram compares to what would be expected for large \(n\) as regulated by the underlying theory.