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I was wondering if there is a known characterization of an arrival process defined as follows: a "potential" arrival occurs according to a Poisson process of rate L, then a Bernoulli RV with P(1)=B determines whether the arrival officially occurs. The Bernoulli RVs are drawn iid. It would be nice if this were itself a Poisson process, but I don't think it is.

Thanks.

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It is a standard exercise to show that this is a Poisson process.

Let $X_t$ be the number of "potential" arrivals before time $t$ and let $Y_t$ be the number of actual arrivals before time $t$. Suppose $0

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    PS: The above counts the potential arrivals that are actual arrivals. Another process counts the potential arrivals that are _not_ actual arrivals. That is of course a Poisson process with rate $(1-B)L$. Here's another exercise: Prove that those two Poisson processes are actually independent of each other.2012-08-11