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

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

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

(2) What are mean value [min] and variance [min²] of the random time Y between the occurrence of two successively recorded particles?