QUESTION: Experiments by Rutherford and Geiger in 1910 showed that the number of alpha particles emitted per unit time in a radioactive process is a random variable having a Poisson distribution. Let X denote the count over one second and suppose it has mean 5. What is the probability of observing fewer than two particles during any given second? What is the P(X > 10)? Let Y denote the count over a separate period of 1.5 seconds. What is P(Y 10)? What is P(X+Y > 10)?

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