Memoryless
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
www.almerja.com
الجزء والصفحة:
...
20-4-2021
1994
Memoryless
A variable 
is memoryless with respect to 
if, for all 
with 
,
 |
(1)
|
Equivalently,
The exponential distribution satisfies
and therefore
is the only memoryless random distribution.
If 
and 
are integers, then the geometric distribution is memoryless. However, since there are two types of geometric distribution (one starting at 0 and the other at 1), two types of definition for memoryless are needed in the integer case. If the definition is as above,
 |
(9)
|
then the geometric distribution that starts at 1 is memoryless. If the definition becomes
 |
(10)
|
then the geometric distribution that starts at 0 is memoryless. Note that these two cases are equivalent in the continuous case.
A useful consequence of the memoryless property is
 |
(11)
|
where 
indicates an expectation value.
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