Cumulative distribution function
Random variables are usually characterized with the Cumulative Distribution Function (or just Distribution Function), and the Probability Density Function, which are related.
The Cumulative Distribution Function is defined with the following expression:
Properties of the distribution function:
- , and
- It is a monotonically increasing function, i.e.
Example: The distribution function of the random variable built assigning numbers to the results of the experiment `throwing a die’ is the following (note that the random variable is discrete):
Figure 2 Cumulative Distribution Function of the random variable of the `throwing a die’ experiment
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