Let us take a look at the following random walk:

\[\begin{equation*} X_{t} = X_{t - 1} + N_{2}(0,\Sigma)~with~\Sigma = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \end{equation*}\]

with \(N_{2}(0,\Sigma)\) being a bivariate normal distribution with mean (0,0) and \(\Sigma\) as variance-covariance matrix. Often the identity matrix \(I\) is used for the bivariate standard normal distribution.

You can see this as a combination of two independent univariate normal distributions, one on the X axis and one on the Y axis, and both with a mean 0 and a standard deviation of 1.

Write a function randomwalk() that takes an argument n and that calculates the first n steps in a two-dimensional random walk. Return the positions at the different timepoints as a matrix with the columns names x and y. Be sure to include the necessary checks and messages for the user.

There is no need to generate an actual nx2 matrix since Dodona will already do that.