Memoryless property distributions

Memoryless Property The exponential distribution shares the memoryless property with the geometric distribution, and it is the only continuous distribution having this property. The proof of the property is simple ... 

One might think that the second probabiUty should be smaller, since the person arrived after the previous bus had left and so there is a smaller chance that he will have to wait for more than 10 minutes. However, because of memoryless property of the exponential distribution... 

It follows from this that the CV of the exponential distribution is 1. The exponential distribution has the remarkable memoryless property, which states that... 

When the chain does leave state i, it chooses its next state j i according to the probabilities exponentially distributed Because the Markov property of X implies that T must have the memoryless property (13), and this in turn implies that T has the exponential distribution. 

As discussed in a previous section, constant rate processes are random events with the memoryless property. This probability distribution appears weU suited to modeling the failures of high-quality devices operating in a benign environment. The constant rate probability distribution, however, does not appear to be well suited to such events as system reconfiguration. Some of these procedures, for example, are fixed time programs. If the system is halfway through a 10-ms procedure, then it is known that the procedure... 

The distribution of the waiting time until first occurrence, given that we have already waited until time t is the same as the distribution of the waiting time starting from 0. The exponential distribution is the only continuous distribution that has this memoryless property. 

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