5. You are studying a linear 1000 bp DNA fragment with two restriction enzyme cut sites at 200 bp and 600 bp from one end of the fragment. If no site is cut, the length of the fragment is 1000bp. If only the first site is cut, fragments of 200bp and 800 bp are produced. If only the second site is cut, fragments of 400 and 600bp are produced. If both sites are cut, one fragment of 200bp and two fragments of 400bp are produced. After incubating with restriction enzyme for 20 minutes, each cut site has a probability p of being cut, producing a mixture of 200, 400, 600, 800 and 1000 bp fragments, depending on whether each site was cut or not. The probability of each site being cut is independent, but occurs with the same probability, p. a) Find the probability distribution of fragment lengths, i.e. P(200), P(400), P(600), P(800), P(1000) in terms of p. Make sure it is a probability distribution. b) After the reaction you run the products on an electrophoresis gel and determine the average fragment length, (L). Find an expression for (L) as a function of p. c) If you have measured that the average fragment length (L) is 500bp, what is p? If your result does not follow directly from part b), justify your reasoning.