Write a program to model a random walk of \(N\) steps, in which each step has the same length \(L\), but is in a random direction in the \(xy\) plane. We will define \(x_F\) as the value of \(x\) at the end of the walk. Your task will be to compute the average value of \(x_F^2\) and the average value of \(x_F\). This will require generating many random \(N\)-step walks to compute those averages.
Plot the average value of \(x_F^2\) as a function of the number of steps taken \(N\), and create a separate plot of the average value of \(x_F\) versus \(N\).