A biassed coin is tossed a total of n+m times and shows Heads (H) with probability p on each toss. Let Kn be the number of heads in the first n coin tosses, and Lm be the number of heads in the last m coin tosses. You may assume that mn. (a) What is the distribution of Kn ? (b) What is the distribution of Lm ? (c) Are Kn and Lm independent? (d) Determine the joint distribution P(Hn=k,Km=) of Hn and Kn. (e) What is the distribution of Hn+Km ? (f) Using a binomial identity on the formula sheet and the joint distribution of Kn and Lm, justify your answer in (e)