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Question 10 A radioactive source emits particles according to a Poisson process with rate two particles per minute. (a) What is the probability that the first particle appears after three min- utes? (b) What is the probability that the first particle appears after three min- utes but before five minutes? (c) What is the probability that exactly one particle is emitted in the in- terval from three to five minutes? (d) What is the probability that exactly one particle is emitted in the inter- val from zero to four minutes, and that exactly one particle is emitted in the interval from three to five minutes