Question: 8.9. Suppose that particles are emitted from a radioactive source and that the num- ber of particles emitted during a one-hour period has a Poisson

8.9. Suppose that particles are emitted from a radioactive source and that the num- ber of particles emitted during a one-hour period has a Poisson distribution with param- eter A. Assume that the counting device recording these emissions occasionally fails to record an emitted particle. Specifically, suppose that any emitted particle has a prob- ability p of being recorded.

(a) If Y is defined as the number of particles recorded, what is an expression for the probability distribution of Y?

(b) Evaluate P(Y 0) if = 4 and p = 0.9.

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