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Determining geig p er counter records

Question:

A Geiger counter is struck by radioactive particles according to a homogeneous Poisson process with intensity per 12 seconds. On average, the Geiger counter λ = 1 only records 4 out of 5 particles.

(1) What is the probability that the Geig p er counter records at least 2 particles a ≥2 minute?

(2) What are mean value [min] and variance [ ] of the random time min Y between 2 the occurrence of two successively recorded particles?

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