November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
Content preview from Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
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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.
- 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, ...
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