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Can you prove mathematically that a geometric random variable possesses the so called Memory-less property?
Wiki User
∙ 13y ago
Proof:
P{T>n+m/T>n}=P{T>n+m,T>n}/P{T>n}
(Bayes theorem)
=P{T>n+m}/P{T>n}
=((1-p)^(n+m))/(1-p)^n = (1-p)^(n+m-n) = (1-p)^m
(1-p)^m = {T>m}
So T>m has the same probability as T>m+n given that T>n, which means it doesn't care (or don't remember) that n phases had passed.
Wiki User
∙ 13y ago
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