3.4 PROBABILITY MASS FUNCTION

An example of the distribution function for a discrete random variable is shown in Figure 3.8. Observe that there are two distinguishing features of this type of distribution function:

FIGURE 3.8 Distribution function for a discrete (Bernoulli) random variable.

ch00.3fig008.eps
  • FX(x) changes instantaneously at values of x that are outcomes of the random variable.
  • FX(x) remains constant between these outcomes.

There are two useful ways of representing the outcomes and the probability assignment for a discrete random variable, using either the Kronecker delta function or the Dirac delta function . The distribution function in Figure 3.8 corresponds to the symmetric Bernoulli random variable with equally likely outcomes . This random variable would arise, for example, when tossing a single fair coin with the mapping: and .

The Kronecker delta function is convenient for representing the outcomes of a discrete random variable because there are no continuity issues. Moreover, ...

Get Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.