Geometric Distribution

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P( ≤ X ≤ ) =

Summary:
If X ~ Geo(p), then P(X = x) = p(1 - p)x-1, where x = 1, 2, 3, ...
It gives the probability that x independent trials are needed to get the first success.


Memoryless properties:
P(X > a + b | X > a) = P(X > b)
P(X ≥ a + b | X > a) = P(X ≥ b)
P(X = a + b | X > a) = P(X = b)
P(X ≥ a + b | X ≥ a) = P(X > b)