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I have a question about computing conditional probabilities of a Poisson distribution.

Say we have a Poisson distribution P(X = x) = e^(−λ)(λx)/(x!) where X is some event.

My question is how would we compute P(X > x1 | X > x2), or more specifically P(X> x1 ∩ X > x2) with x1 > x2?

I originally thought that P(X > x1 ∩ X > x2) = P(X > x1) but recently read about the memorylessness property of exponential distributions and I'm not sure if it applies to Poisson distributions.

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# I Poisson distribution with conditional probability

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