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
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B.13 INDICATOR FUNCTIONS
Definition: Indicator Function The indicator function for set E is
(B.64) 
When E = [a, b] for a<b, the indicator function specifies a closed interval:
(B.65) 
Open and semi-open intervals are similarly given by I[a,b)(x), I(a,b](x), and I(a,b)(x). It is possible for 
or 
or both, in which case we might use 
. The indicator function can be written in terms of the unit-step function as follows:
(B.66) 
It can also be used for countable sets 
such as
(B.67) 
where brackets have been used to emphasize that x is discrete. The indicator function is convenient for specifying the support of a pdf (for the exponential random variable):
(B.68)
or a pmf (for the Poisson random ...
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