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Mathematics, 22.01.2020 00:31 cathydaves
Show that if x ∼ geom(p) then p(x = n + k|x > n) = p(x = k), for every n, k ≥ 1. this one of the ways to define the memoryless property of the geometric distribution. it states the following: given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.
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Show that if x ∼ geom(p) then p(x = n + k|x > n) = p(x = k), for every n, k ≥ 1. this one of the...
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