The horizontal axis is the index , the number of occurrences. The CDF is discontinuous at the integers of and flat everywhere else because a variable that is Poisson distributed takes on only integer values. (en)
The horizontal axis is the index , the number of occurrences. is the expected rate of occurrences. The vertical axis is the probability of occurrences given . The function is defined only at integer values of ; the connecting lines are only guides for the eye. (en)