2. A random experiment is repeated n times. In each experiment, the probability of success is p. The outcomes of the experiment are observed and recorded. Let X be the number of the observed successes. a) Write down the probability py = Pr (X = k). Describe the general trend of Pk. b) Determine the (integer) value of k such that p, is a maximum for a fixed n. c) Determine the condition that there exist two possible (integer) values of k yielding the same maximum