- a function of a continuous variable whose integral over a region gives the probability that a random variable falls within the region.
- a function of a discrete variable whose sum over a discrete set gives the probability of occurrence of a specified value.
- a function representing the relative distribution of frequency of a continuous random variable from which parameters such as its mean and variance can be derived and having the property that its integral from a to b is the probability that the variable lies in this interval. Its graph is the limiting case of a histogram as the amount of data increases and the class intervals decrease in size
