Probability Distribution Function for continuous random variable is called Probability Density Function while the one for discrete random variables is called the Probability Mass Function.
The probability distribution function is mainly characterized by cumulative distribution function which represents the summation of probabilities of all possible events.
e.g.)Discrete Distribution Function:
Consider an example of discrete probability distribution function. The figure below shows the probability of selling a specific number of bikes by a dealer per day. The X-axis has all the possible number of bikes sold and corresponding probabilities are represented in Y-axis.