Lack of Memory Property

"For x, y > 0,

P [ X > x + y | X > x] = P [ X > y]

We can interpret this as follows.  Suppose that X represents the time, measured from now, in weeks until the next insurance claim is filed by a company, and suppose also that X has an exponential distribution with mean 1/t.  Suppose that 5 weeks have passed without an insurance claim, and we want to know the distribution of the time until the next insurance claim as measured from our new time origin, which is 5 weeks after the previous time origin.  According to the lack of memory property, the fact that there have been no claims in the past 5 weeks is irrelevant, and measuring time starting from our new time origin, the time until the next claim is exponential with the same mean 1/t.  In fact, no matter how many claims have occured in the past 5 weeks, as measured from now, the time until the next claim has an exponential distribution with mean 1/t; the distribution has "forgotten" what has happened prior to now and the "clock" measuring time until the next claim is restarted now."

Peace out.