Consider the mode m of the binomial (n, p) distribution. use the formula m = int (np +p) to show the following:
a) If np happens to be an integer, then m = np.
b) If np is not an integer, then the most likely number of successes m is one of the two integers to either side of np.
c) Show by examples that m is to necessarily the closest integer to np. Neither is m always the integer above np, nor the integer below it.