2. memoryless distributions Suppose that, for every length of time, s2 0 andt2 0

Question

2. memoryless distributions Suppose that, for every length of time, s2 0 andt2 0, the probability that T survive longer than s+t given that it had already survived longer than s is exactly the same as the simple probability that it merely survive longer than t: PlT > s+t | T > s) = P(T > t) > 0 Ys-0,120 a) If T is discrete with P(TEN) 1, what must be the distribution of this T? b) If, however, the survival function, F(t)- P(T>t), were continuous in t 0, what then must be the distribution?

Explanation / Answer

a) Geometric distribution

b) Exponential distribution

In distribution theory, memory less is a property of certain probability distributions. It usually refers to the cases when the distribution of a "waiting time" until a certain event, does not depend on how much time has elapsed already. Only two kinds of distributions are memory less. One is exponential distribution of non-negative real numbers and the geometric distribution of non-negative integers.

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