Regarding Poisson process

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The number of cars which pass a roadside speed camera are assumed to behave as a Poisson process with intensity λ. It is found that the probability that a car exceeds the designated speed limit is p.

  1. Show that the number of cars which break the speed limit also form a Poisson process.

  2. If n cars pass the camera in time t, find the probability function for the number of cars which exceed the speed limit.