Simulate a discrete random walk in Z2 starting at the origin and moving north with probability p1=0.30, south with p2=0.05, east with p3=0.75, and west with p4=0.81. For your random walk,

(a)

Plot 5 realisations of your walk with 2500 steps on the same plot (it may be wise to use dierent colours for each random walk).

(b)

Calculate the expected length of the walk after 2500 steps (i.e. the distance travelled from the starting point). [You will need to run many walks to get an accurate estimate, experiment with the number of walks until you get a number that gives a suciently stable expectation value. You can also choose whatever distance measure you wish]

Please state clearly the choices you have made and and values used.