Why is waiting time memoryless? (in Stochastic Processes)

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SUMMARY

The concept of memoryless waiting time is a fundamental characteristic of certain stochastic processes, specifically those modeled by exponential distributions. In these processes, the probability of an event occurring in the next time interval remains constant, regardless of how much time has already elapsed. This principle is exemplified in scenarios such as the lifespan of a light bulb, where the likelihood of it functioning for an additional period does not depend on its previous operational time. Understanding this concept is crucial for accurately applying stochastic models in various fields.

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I am learning Stochastic Processes right now. Can someone some explain why waiting time is memoryless? Say, if a light bulb has been on for 10 hours, the probability that it will be on for another 5 is the same as the 1st 5 hours.
It doesn't make sense to me, because the longer you use it, the more likely it will break down. No?
 
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Waiting time is memory-less for processes that have been defined to be such. As you observed there are processes which may not be.
 
got it, thanks!
 

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