In the lectures we estimated the value of using de Buffon's needle. Here we will use an alternative approach. In the diagram below, we have a circle of radius 1.0, enclosed by a 22 square (in some arbitrary units). The area of the circle is r2= and the area of the square is 4 (in units squared). If we divide the area of the circle, by the area of the square we get 4 For a very large number of points, we have areaofsquareareaofcircle=4=numpointsinsquarenumpointsincircle If you sequentially select points within the square at random, the state of the point being within the circle constitutes a Markov chain. Generate 5 Markov Chains by randomly picking points and calculating the ratio of those that fall within the circle to the total number of points selected, this is (you may prefer to multiply the ratio by 4 so it approaches ) (a) Generate 5 chains, calculate the value of after a large number of steps (you are free to choose how long this should be and you should state the burn-in for each chain). (b) Calculate the within and between chain variances