memoryless random variable
In words, given that a certain event did not occur during time period in the past, the chance that an event will occur after an additional time period in the future is the same as the chance that the event would occur after a time period from the beginning, regardless of how long or how short the time period is; the memory is erased.
From the definition, we see that
so iff is memoryless.
An example of a discrete memoryless random variable is the geometric random variable, since , where is the probability of =success. The exponential random variable is an example of a continuous memoryless random variable, which can be proved similarly with replaced by . In fact, the exponential random variable is the only continuous random variable having the memoryless property.
|Title||memoryless random variable|
|Date of creation||2013-03-22 14:39:49|
|Last modified on||2013-03-22 14:39:49|
|Last modified by||CWoo (3771)|